房客会还吗？

Two possible developments:

1.  landlord, I need the signed lease back, tenant: okay, here it is, signed. 

2.  landlord, I need the signed lease back, tenant: (silence or BS or no action); landlord, I asked the second time, I need the signed lease back; tenant: (silence or BS or no action).  Landlord, sending a registered letter saying he needed the lease, or he would treat it as unsigned and the tenancy is month-to-month.  

Tenant:  (silence, BS or no action),  Landlord can send notice to end tenancy. 

I don't think tenant will return the unsigned lease.  But if she did, congrats.