Leaving BC

All foreign nationals

Close your bank account and inform the HR DEPARTMENT about the number of your foreign bank account for the last payment / settlement
Get confirmation of participation in the pension system
Get employment certificate
Tax reimbursement (if relevant)

EU Nationals

If you are employed, inform your employer about your departure (unless you are leaving at the end of your contract with them). Usually you must give them a full two months notice (starting on 1st of month following the date when you inform them). Alternatively, arrange to have unpaid leave while you'll be abroad.
If you have been studying in the Czech Republic, inform your institution of your wish to suspend or terminate your study. If you have children who have been at school in the Czech Republic, take copies of their latest reports and information about the curriculum they have studied with you to give to their new school.
If you have a temporary residence card and you are sure you will be away from the Czech Republic for more than 180 days, you must inform the ministry at least three days before you leave the country, and must return your temporary residence card (the competent HR department staff can do this for you if you give him/her written authorization to do so).
If you have permanent residence in the Czech Republic you can retain this permanent residence beyond your departure, if you still have your address (place of "usual residence") in the Czech Republic, and as long as you won't be outside the EU for more than 12 months. Otherwise you should also inform the Ministry of your permanent departure for another country and return your residence card (or authorize the competent HR department staff in writing to do so in your stead).
Inform your health insurance provider and the social security office of the date when you will be leaving. If you are employed, your employer will usually inform the social security office for you. If you will not be returning to the Czech Republic (or not for six months at least) you will need to complete a departure form for the health insurance and return your health insurance card.
Check whether you will still be tax resident in the Czech Republic (for the year you leave and/or in future). For more information about tax residency and the tax procedures in the country where you are going, contact the financial authorities there (and/or here).
You may wish to terminate your rental contract (if living in rented accommodation), your bank account(s), and any contracts with service providers (e.g. electricity, internet, telephone, insurances), club memberships and so on.
Ensure your passport is valid for at least 6 months (if you are travelling outside the EU). Obtain copies of your ID documents in case you lose them.
Apply for any visas you require for your intended destination.
Inform your doctor(s) and dentist of your departure. You may wish to request a copy of your records from them for your new doctors.
Sell your car or inform Czech registration authority that you are removing your car from the Czech Republic and cancel any parking permits you no longer require.
Inform anyone who might need to contact you about your new address and consider re-directing your mail. If mail will still be sent to a Czech address for you, make sure you give formal authorization to someone at that address to receive mail on your behalf.
If you subscribe to any regular magazines or periodicals, unsubscribe or change the adress, or if possible arrange to have them sent to you electronically.

https://www.mvcr.cz/mvcren/article/ending-and-revoking-a-residence-permit-and-leaving-the-cr.aspx?q=Y2hudW09Mg%3d%3d

Nationals of non-EU countries

If you are employed, inform your employer about your departure (unless you are leaving at the end of your contract with them). Usually you must give them a full two months notice (starting on 1st of month following the date when you inform them). Alternatively, arrange to have unpaid leave while you'll be abroad.
If you have been studying in the Czech Republic, inform your institution of your wish to suspend or terminate your study.
If you have children who have been at school in the Czech Republic, take copies of their latest reports and information about the curriculum they have studied with you to give to their new school.
If you have a scientific permit or other long term residence permit, work permit etc. you must return your residence card to the Ministry of Interior at least three days before you leave the country. You can also give the card to the competent HR department staff (with a power of attorney), and she/he will return it for you on the date of your departure.
If you have permanent residence in the Czech Republic you can retain this permanent residence beyond your departure, if you still have your address (place of "usual residence") in the Czech Republic, and as long as you won't be outside the EU for more than 12 months. Otherwise you should also inform the Ministry of your permanent departure for another country and return your residence card (or authorize the competent HR department staff in writing to do so in your stead).
Inform your health insurance provider and the social security office of the date when you will be leaving. If you are employed, your employer will usually inform the social security office for you. If you will not be returning to the Czech Republic (or not for six months at least) you will need to complete a departure form for the health insurance and return your health insurance card.
Check whether you will still be tax resident in the Czech Republic (for the year you leave and/or in future). For more information about tax residency and the tax procedures in the country where you are going, contact the financial authorities there (and/or here).
You may wish to terminate your rental contract (if living in rented accommodation), your bank account(s), and any contracts with service providers (e.g. electricity, internet, telephone, insurances), club memberships and so on.
Ensure your passport is valid for at least 6 months (if you are travelling outside the EU). Obtain copies of your ID documents in case you lose them.
Apply for any visas you require for your intended destination.
Inform your doctor(s) and dentist of your departure. You may wish to request a copy of your records from them for your new doctors.
Sell your car or inform Czech registration authority that you are removing your car from the Czech Republic and cancel any parking permits you no longer require.
Inform anyone who might need to contact you about your new address and consider re-directing your mail. If mail will still be sent to a Czech address for you, make sure you give formal authorization to someone at that address to receive mail on your behalf.
If you subscribe to any regular magazines or periodicals, unsubscribe or change the adress, or if possible arrange to have them sent to you electronically.