When you get the "gift" from Ezic, you get the option to burn it on both occasions.
If you don't burn it, you'll be reported by your neighbors and lose your savings for you "suspicious wealth".
Is there a way to keep the money and still play the game to the last day?
Sadly, there is no way.
Source: Papers Please Wiki
Is there any way to keep the 1000 or 2000 credit EZIC gift?
No. The EZIC money you receive on day 11 or 12 will always be confiscated, together with any other savings you have. Your neighbour always "reports you for your wealth", even if you have done nothing to appear wealthy. Allowing an EZIC agent (Stepheni Graire) to enter the country will prevent you being arrested for receiving the money, but it will not allow you to get the money back. If you burn the money, you will get to keep your other savings.
The other answers are correct in that you are not able to keep the 1000 or $2000 gift given to you by EZIC. This is because the inspector's savings will be confiscated.
However, there is a way to retain $75 of those credits, which is already a big bonus if you're not playing on Easy Mode.
This is done by upgrading to a class-7 apartment on day 12, then downgrading back to class-8 immediately the day after. By doing this, you are practically investing your money in the apartment, and then dropping out after your savings are confiscated.
