To what degree is a victim of unfortunate circumstances morally obligated to "be strong" for the people around him/her?

This is kind of hard to explain.

Say you’re ill, or you’ve just suffered a loss, or something else awful is happening to you that has you really down in the dumps. Ideally we’d hope that your loved ones would be strong for your sake – you need support right now. But if your loved ones just don’t have that kind of strength, or if the situation goes on for so long that they burn out, or your depressive mindset starts rubbing off on them, or they just feel so sorry for you that it’s tearing them up – what then? Are you morally obligated to try to reverse the roles and be strong for them? Put on the happy face so that they don’t have to feel sorry for you anymore? Or does being the victim of an unfortunate event give you the right to keep leaning, even if you feel your weight may knock your loved ones over?