If the extractor snaps easily over the rim and chambers, sound more like it might be excessive headspace- round is able to be pushed further forward than should be, so the extractor can't grab the rim.
Take some cellophane package tape, cut a small piece and stick it over the end of the dummy round or sized case (recommend not doing this with a live round- but if you must do it safely). Trim the tape all around the case with a new razor blade. Do it again, for a second layer.
Disassemble the bolt. Youll need to either notch the rim of a sized empty case so the extractor doesnt interfere, or remove the extractor which can get a bit hairy since you dont have the coin gauge with a notch in it. The extractors will bend, and somerimes snap if youre not careful. if you remove it, bend back slightly and pit a few drops of kroil in there before trying to drive it down and out- it's a dovetail fit. Slip the round by hand into the chamber, then slide the bolt into the receiver, push all the way forward and gently begin to lower the bolt handle. If you can put it into battery without resistance, add another layer of tape, and repeat. If it still closes, you've probably got excessive headspace...
Each layer of tape is .003-.004 thick on average, closing on even two layers is questionable and three would be indicative of the problem.
This can happen from lug setback- but also from a "mixmaster" rifle where someone has swapped the bolthead without checking headspace after. Just like a Savage, these rifles have floating boltheads (which allows these receivers to be built into pretty accurate rifles for those that wish to do so) and dimensions vary by as much as 6 thou or more.
Hope this helps...