I'm not sure if dogs are the same way, but un-fixed cats (male or female) will pee on everything. 

The female tenant said she would like to stay and would like to find a new roommate. 

Hi, I currently live in the San Francisco Bay area, which is extremely expensive for a single female.

You should try to identify what market you want to get into first, college rentals, vacation rentals, young professionals, familys, military, latino areas, asian areas, section 8, la jolla upscale. 

@Karan Rekhi this is all i do. i only rent by the room. anyone that tells you it’s not worth doing is wrong. be careful about town ordinances. the town i am in only allows 4 unrelated people per unit.as far as finding people, i do all of that although your incentive idea isn’t terrible. i have all multifamily and i basically position tenants together that will fit well. also, sometimes females will be uncomfortable living with males. for the most part, if you can get like minded people together you will be fine.yes, depending on your class of people, you will get some drama. do your homework on your tenants and vet them well and always talk to the previous landlord. happy to help you here. just let me know why other questions you have. you will have growing pains with this strategy but once you get the hang of it, it will be very valuable.

The tenants know the LL is a slumlord (the tenant handyman has done work for the slumlord and both (the male and female tenant) know the condition of his units). 

I also give them discretion to reschedule if the only person home is a young female.  

@Steven May find a female (or whatever) that is onboard with you.

The young female tenant is nervous because of odd behavior of a male tenant who lives in another unit at the same property (directly across the hall). 

And that's worked well for me as a female investor/property manager.