Half cook meat and then fully cook it?

My grandma half cooked frozen sausages this morning. She stuck them in the fridge and they have been in there for 6 hours, half cooked. She now plans to " fully" cook them by broiling them in the oven. Are these safe to eat? Can I get food poisoning or anything like that by eating meat that was half cooked, refrigerated, and the cooked again? Thanks.