I was wondering if comb-footed/cobweb house spiders can scavenge dead insects or if they just eat live insects?

There are a ton of spiders in this Family.

Try Cobweb Spiders - Learn About Cobweb Spiders, Family Theridiidae (http://insects.about.com/od/spiders/p/theridiidae.htm) and other simlar web sites there is much information if you do a search on "comb-footed/cobweb house spider".