Do they have a job? Are they going to pay rent? Are they going to trash the place? Do they have a criminal background? Do they use drugs? Are they going to bring a pet in? Who is going to pay for any damages? (The new guy is going to blame you, and you are going to blame him.)

It's absolutely legal for an owner to not allow subletting. Legally the new tenant hasn't signed a contract and it leaves the owner (and you) exposed legally. It's hard enough when the owner screens the renters. I would never allow subletting.

Having said that, in an apartment complex situation where there are multiple tenants in one apartment, like BYU student housing, it probably happens.