Breed? Age? If otherwise of good temperament, do you have the option of creating a secure fenced area? Otherwise, can you try to re-home her or find a no-kill shelter that can take her.
Lots of options to explore before putting down a dog. You’ll never find a more loyal companion, and they deserve a better fate.
I’m in a house rental and it would be expensive to install a fence, besides, the landlord doesn’t want one.