Is there a way to keep the EZIC gift?

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.