Also consider that this tenant has a tad bit lower credit score than I'd prefer but pre paid a couple of months worth of rent already. 

In that case, I will use the prepaid rent to cover the monthly rent loss but once I have the property rented and say I have a balance of 3 months of rent left, does the remaining prepaid rent money go back to the tenant, if I find them?

I then let the surplus bank as extra pre-paid rent as they get back on their feet.The small raise also becomes an expected annual thing.  

I echo the above, except the title co. did their job properly.....they deducted/transferred deposits, I assume prorated rents, but they had no evidence or instructions about prepaid last month rents as the buyer didn't know of their existence, and that is the buyer's job to determine, not the title co.

It covers issues such as rental agreements, security deposits, prepaid rent, evictions, installment contracts, credit card interest rates, mortgage interest rates, mortgage foreclosures, civil judicial proceedings, automobile leases, life insurance, health insurance and income tax payments.

Did you get the tenants’ security deposit and pre-paid rent (if any) from the seller?

Some areas do limit amounts of deposits, but I haven't heard of anywhere that limits prepaid rents.4.  

On the rare occasion when a tenant needs to pay otherwise, it's a one-time deal (like changing bank accounts or such), and they're back on track the next month.ClearNow lets you draft from many sources: bank/savings accounts, pre-paid debit cards, etc.I have a tenant who has been struggling lately.

She may have even prepaid the rent before going on vacation and the previous owner forgot or "forgot." 

Another option is have them get a NetSpend card or a similar prepaid debit card that allows ACH debits and they can use that with a payment service, such as PayPal or a rent payment service.