If you're being evicted you still should pay any rent owed for the time you have stayed in the apartment or house.
If you don't pay the rent you owe even when being evicted the landlord or property manager can take you to court again and sue you and garnish your wages or levy your bank account to pay for the rent payments owed to them.
Some landlords however will just write it off and move onto the next tenant but for your rent history you should go ahead and pay the late rent owed or any other pass due rent owed to the landlord so that you have a good rental history.
You still do owe the rent even when being evicted especially if you're being evicted for non payment of rent.
Even if you were to make payment arrangements and pay at least some each month to the landlord for the rent it's better than not paying any rent at all even when you're being evicted.