This is an extremely thorny family situation probably best dealt with by seeing a therapist who can help you sort out the complexities of your feelings, the relationship, and the different courses of action you can choose in the present situation.  That said, I can offer some general comments about your situation and some questions for you to ponder as you work through your decision-making process.

It is hard to come up with meaningful advice in the absence of so much critical information. For example, how do you feel about your sister at this point in time?  Have you come to peace with her rejection or do you still hold active anger and resentment toward her?  What are your own financial circumstances?  Do you have a partner and/or children to support? Do you have any true discretionary funds to lend or gift to your sister should you decide to help her?  How truly urgent is her situation and does she have other resources available to meet her short-term needs? These and many other questions will have a direct bearing on how you answer her.

In general, I advise people to give of themselves and their resources when they can do so without feeling resentful or exploited (used) by the person asking the favor.  I also encourage people not to answer immediately but to take a bit of time and talk with your partner, your close friends, and/or a therapist to sort out your complicated feelings.  Visualize different ways of responding to her in your mind and see how each scenario sits with you emotionally.  Which of several scenarios leaves you feeling best about yourself and best about the situation?  That is probably the course of action to follow.

This could be an opportunity to initiate healing in your relationship with your sister, or it could be the beginning of a new chapter of painful relating and ongoing financial dependency of your sister upon you and your family.  If you choose to make a gift, a loan, or provide ongoing assistance for a period of time, be clear with yourself and clear with her which of these you are choosing to do.  If it is a loan, it is best to draw up an appropriate legal contract for a personal loan so that the terms are absolutely clear.  If she is not willing to draw up such an agreement, you can be pretty certain that she is really looking for a gift, not a loan. Are you willing to do this?

Finally, although it is very difficult, it may be helpful to separate the unresolved issues in the relationship from the financial issues and decide what you need to address. Do you need the relationship issues to be addressed before considering her request for financial assistance?  Are you willing to offer financial assistance regardless of whether the relationship issues are addressed?  These are extremely important things for you to get clear about before acting. Then check in with her and see what is possible.  Be clear with yourself about your feelings and expectations (both those you are aware of and those you are unconscious of) and ask yourself if your hopes and expectations are realistic.

Ultimately, you are the person you will have to account to for whatever choice you make. It is important that your choice be well-considered, non-destructive, and one you can live with in relative peace after you have made it.  I wish you the best.