I am sure that the agents wouldn't be too happy if a person accepted a bid that was just what they owed on the home, then there was no money to pay them. Not to mention the fact that if it is a short sale, the buyer would have to pay any transfer taxes that are due.
If you are currently working with a Realtor they can check that for you and explain the process.
You can also check the public records. However, I think working with a professional is your best bet.
Let's say the property is priced right - at the current market value. If you decide to offer less that the seller's current mortgage balance, the seller may not accept the offer. If the property is priced way above market value and and you offer less but the mortgage balance is higher than your offer, then it is up to the seller what he/she decides to do.There could be many different scenarios in this case. Everything depends on the motivation to sell. If the seller really needs to move out of the property they may consider a short sale in that situation. Your Realtor can negotiate that for you. Short sales can be very complicated at times, so it might take a long time to close that deal. Every case is different.
I hope that answers your question to some point. Let me know if you need more details.
If the property is in Miami-Dade, I included web reference to Miami Dade public records.
This should be noted in the listing if it is a possible short sale. If it ends up being a short sale, then the bank will have to approve your offer. It could be months before you get an approval.