The answer is: it depends.
If you simply cash it the landlord may claim you have settled the whole matter by accepting a partial payment. Landlord might even lie and say you orally agreed to accept the payment as settling the claim.
If you see the words “full and final payment” or “final settlement” or something like that anywhere on the check, definitely don’t cash it. That’s them trying to trick you into signing an endorsement that the whole thing is settled.
It might not look exactly like those pictures, but words like that are what you’re looking for. If it doesn’t say anything like that anywhere on the check, or in any paperwork that came with it, you should still be able to accept the partial payment while notifying the landlord explicitly in writing that more is still owed. (You can do this with our DepositLetter assistant.)
Simplest would be to cash the check and write above your signature on the back “accepted as partial payment of debt owed”. And be sure to take a picture of both side of the check for your records.
A bird in the hand is worth two in the bush. You have to weigh the money in hand vs. the potential difficulty of getting more. Depending on how little it is, I would put it in the bank.