Contact the bank that is doing the foreclosure and see if they will allow you to assume the mortgage or purchase the home. You can bid on the property at the auction. They may want you to stay in the house and perhaps pay rent so the property does not become derelict.
Contact the lender about purchasing the home or assuming the mortgage. If you can't work something out then show up at the auction and bid on the property. Another option is to have you sister contact a bankruptcy attorney about filing a Chapter 13 case to stop the foreclosure sale. If she is willing to do that you can make arrangements with her to pay the monthly payments to the trustee and the mortgage during the case. If you stop the sale it will also buy your sister more time to try to work out a deal with the lender such as a modification. Good luck.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Unfortunately, it is not likely that you will get very far trying to contact the bank or mortgage company. The mortgage company who is foreclosing on your sister is not likely to be cooperative in even responding to you. What you are most likely to get is nothing except frustration. And if your credit is not good, the odds of your getting a loan are slim. Otherwise, you might be able to consummate a short sale, however this always entails getting your own mortgage loan. Prior to foreclosure being completed at times the mortgage company will sell the mortgage to an interested party, but only for cash in a lump sum. It does not sound like that will be feasible for you. Once the foreclosure is complete, the house will be put on the market, and generally the asking price will wind up much lower than the total debt.
Your best bet is to see if you can quickly get your credit repaired (but be careful and make sure that you only deal with a legitimate credit attorney). If you can get this done, you might be able to qualify for a loan to buy the house after the foreclosure sale. If you can get your credit cleaned up quickly enough, you might be able to get financing and buy via a short sale before the foreclosure is completed.
Anyone who has ever tried will tell you that the mortgage companies are a nightmare to deal with, and will not do anything that is "out of the box". They understand short sales, and they understand REO sales (a sale where you buy from the mortgage company after the foreclosure is over, assuming the mortgage company buys the house at the foreclosure sale, which is the norm these days). So, your best bet is to position yourself to speak to them in a language they understand, which means either via short sale or REO.
P.S. While a Chapter 13 by your sister might work, if it does, you will not be the owner, she will, unless at some point she sells it to you and pays off the mortgage. If the property is worth less than the mortgage debt, as so many in Florida are these days, that is not likely to be an economically viable solution even if technically possible. The first place to start in such an analysis is to ask your sister to get a payoff statement from her mortgage company and to do some homework to ascertain what the current market value of the house is right now - meaning, what it could be sold for. The real estate market in Florida is bad right now, and the Orlando area is one that is particularly bad, so odds are good that the property is upside down. Since Congress did not approve the bill which would have allowed bankruptcy judges to reduce residential first mortgage debts to the current market value of the property, a Chapter 13 would not fix that imbalance. However, if there are two mortgages on the property, and if the house is worth less than the first mortgage but not by too much, that might change the picture.
You and your sister should speak to an attorney who is experienced in Chapter 13 proceedings to ascertain what the realities of such a plan would be in your case. If this turns out not to be a viable alternative, then you are stuck with either a short sale or buying from the mortgage company as an REO property after foreclosure.