Some people actually appreciate (or at least enjoy) the pity of others (especially when such amounts to material benefit). Feeling depressed 'can' foster an inclination towards accepting or seeking sympathy. For these it can be difficult to ween themselves off such dependency - as in a sense such is their quality-of-life-support, and the healing process can take much longer.

I personally think that it comes down to one's viewpoint on life. A persons with a modest degree of pride will have mixed feelings about receiving pity.

It is true though that it is possible to pull one's 'sympathy muscle' and there is such a thing as 'overstaying one's welcome'.

Thank you for giving this a read and for the up-vote @macchiata! :c)