Or is it because the doorway is not sealed properly and somehow the rain water is getting into only that closet?

: There were screens missing from some of the windows upon move-in which we authorized maintenance to replace (they were backed up several weeks due to COVID shut down), A/C wasn't getting the apartment cold enough even though it had been serviced within the past year (set at 68F during the hottest summer we've had in years in Michigan) and we didn't offer to pay her electric bill, found a bat in the basement x 2 which we had professional pest control there at their first available appointment and they didn't find any evidence of a colony but we had maintenance seal off any areas in the basement that could allow bats in, and now a water leak from upstairs apartment overflowing their toilet onto this tenant's mattress.  

:As of July 11, 2019, the Human Rights Law prohibits discrimination in public and private housing based on a favorably resolved arrest record, an adjournment in contemplation of dismissal, a sealed conviction record, or a youthful offender adjudication.

I also used three coats of arm r seal on top it.

Just be SURE to seal the whole sucker in grout sealer (tile & all) so it is an easy cleanup between tenants.

It seems the grout always looks horrible, sealed or not.  

Nobody can do anything about the humidity unless the house is kept 100% sealed.

I can seal them weekly for the first month, but once tenants are in then sealing them regularly after that is going to be really hard.

You can also advertise as Coming Soon- possibly give you and your current tenant time to get the property in show shape.I love when properties are vacant unless the tenant is into staging and helping you seal the deal. 😉

If mice become an issue (so far only in one house) we will set traps and seal possible openings.I once had a tenant who moved from New Jersey who, I learned (AFTER the lease signing of course) had very bad OCD and was terrified to the grasshoppers outside.