If you allow your current house to go to foreclosure, you will probably find it impossible to get another loan to buy something else. If your credit is bad, you may be unable to get financing to buy something else anyway. You would do better to find a tenant for your current house if that will cover your payments.
Foreclosure is a lawsuit which, If not interfered with, this results in a foreclosure sale being held and the Ihouse being sold, usually to the lender, who then evicts any inhabitants and puts the property on the market as "bank owned". Eventually this leads to a sale to a new owner.
After that, the lender can take steps to obtain a deficiency judgment against you if it has not recovered the entire debt, which these days in Florida is the norm. Florida law makes the process of obtaining a deficiency judgment quite straightforward. All of the foreclosure complaints I see these days contain right in the a request for deficiency judgment. Once the foreclosure is over, the lender can come back to the court with the total amount of the debt, plus all accrued interest, costs, attorneys' fees, advances for taxes, insurance, realtors' commissions etc, and deduct from that the amount it got for the property through foreclosure, and ask for judgment for the difference. Once it gets the judgment, it can use that to levy on other non-exempt assets of the debtor, including real estate, bank accounts, vehicles, jewelry, etc. It can take that judgment to any other state in the US where the debtor may have assets, domesticate it there, and then use it to levy on non-exempt assets there.
So, the answer is YES, the bank can come after you. Unfortunately, there is a great deal of misunderstanding of this process, by people who believe that this will not happen, and who "let" a lender foreclose, thinking they can just walk away from the mortgage obligations without further consequences. That is incorrect. I am already seeing borrowers being pursued for deficiency judgments.
Florida judgments are effective for 10 years after entry, renewable for another 10. The lender has 5 years after foreclosure during which it can begin to pursue a deficiency judgment. People who think that allowing the lender to foreclose ends the entire issue are likely to be in for a very unpleasant surprise if they think the issue is over. It used to be the case that deficiency judgments were rare, because it used to be the case that properties were bringing significantly less than what was owed. Therefore, it used to be true that the foreclosure and sale of the property made the lender whole. Therefore, there was no need for deficiency judgment to come up. Now, of course, that has all changed.
Your best defense against a deficiency judgment is to get an attorney who is a specialist in foreclosure defense to find as many issues as possible that the lender has done wrong, and to aggressively defend the foreclosure action. It may be possible that this will ulitmately lead to a negotiated resolution where the issues you have are resolved and the lender agrees to waive a deficiency judgment in return.
Whether you can do a short sale or not depends on many things. There are lots of realtors trying to convince homeonwers that short sale is the solution to their problem. This is rarely true. A successful short sale involves having your lender's consent (hard to get) and having a buyer and a contract (also hard to get). Very few of these work out.
Your best option is to get a capable foreclosure defense attorney to raise as many appropriate issues as possible and to attempt to negotiate a reasomable solution for you. That is what we are doing for many people in this situation. If we can help you, our contact information is on our web site, www.golantlaw.com