Like* teacup* stated, lots of different scenarios, so it depends. I've turned down plenty- sometimes suggesting a different/better place to donate. I've accepted then passed on, donated, or otherwise disposed of and I've accepted, kept and used. There have been a couple situations where I was invited to look through & take what I wanted and I have happily done that too.
I recently had a family member ( I've not seen had contact with in 15 years) send me a message saying she had an old quilt top and a bunch of material she didn't want ( she doesn't sew at all), would I like the stuff? I hesitantly said I guess.... She happend to be at a family get together, asked my sister if she could get this to me. Sister said yes. When my sister later went to her car she found the whole trunk and backseat crammed full of garbage bags.... YIKES! What the heck- she went back in & asked about it- the answer.... I cleaned out my closet and since Colleen sews I thought she could cut the stuff up- I didn't want to give it to goodwill- they charge too much for clothes....
My sister who happens to drive by salvation army store on her way to work stopped in the next day and dropped off all the bags of clothes- kept the bag that was ( supposed to be) the quilt top.
( I bless my sister every day!) The quilt top turned out to be a big comforter someone cut one end off from...
You just never know.....