It depends...who is doing the offering and why.
Is it a family member who would be hurt if you decline the offering? That's the hardest one.
Or is it someone you don't know well?
Did someone find something "wonderful" at a yard sale, etc. and pick it up for you, just sure you'd love it, and you feel obligated?
Are there strings attached...expectations that you will treasure whatever the item is and never get rid of it? Would they be offended if you re-gift, sell or otherwise dispose of the item?
Or is it from someone who just wants to re-home something and is not concerned with what happens next?
I was gifted with part of a stash of a deceased quilter I never knew met. A friend ran into the woman's family members desperately trying to clear out her apartment. My friend does not sew, but she split the stash between me and another quilter. Luckily the fabric came from smoke-free home and most of it was great. However, I'm going to re-home some of the fabric and sewing notions I'll never use.