A bank or credit card agency can deny your application for pretty much any reason. That said, it's extremely unlikely they'd do so for a secured credit card. This is because the credit is secured. If your sister is to get a card with, say, a $1000 limit, she will have to provide $1000 in security. This means the banks risk practically nothing. That said, I have found one reference that claims you need a score of above 600 to qualify for a secured credit card, though this is hard to believe.
Secured credit cards are a reasonable way of building your credit back up. Just about the only other way for her credit rating to improve is for her history of bad debt to fall off the credit report, but that's going to take quite some time. She should be working hard to provide positive credit history to replace the old negative history, assuming her credit rating is important to her. It may not be; it's only important if she plans on taking on debt in the future.
Honestly, a credit rating of around 500 is so bad that I wouldn't even worry much about lowering it. It's already low enough as to make it all but impossible to qualify for (unsecured) credit or loans. A single denial is unlikely to significantly affect the score, except in the very short term.
With two bankruptcies, I encourage credit counselling for your sister. There are a number of good books available, too. Credit counselling should go into detail on credit scores, unsecured credit, proper budgeting, and all that sort of useful information.