Can you get approved to rent an apartment while collecting unemployment?

It would depend on the requirements of your new landlord. Since rents are ussually paid in advance it is not like the landlord is issuing credit. The landlord may want to validate the renter ablility to pay and payment history to insure the landlord is renting to someone he will not have to evict in 30 days. Contact the landlord and let hime/her understand your situation.