The driver was wrong to leave the package if "signature required", period. That should be enough to get someone fired and depending on the package contents, worse.
I have never had a package left if no one was at home per Fedex delivery if signature was required, and could either pick it up at the main delivery depot if within Fedex working hours, or try to be available when they attempt re-delivery on the following day. Sometimes calling (if you have the tracking number) they will stop back by.
Airborne Express was terrible, much better after DHL took over them (until they stopped domestic delivery and laid off 8000 personnel in Wilmington, Ohio).
BTW, I have plenty of packages delivered on weekends (Saturdays) and they don't waste time if you don't answer the door promptly, gone pretty quick.
I also like dogs but was bit by enough delivering newspapers as a teenager that I wouldn't waste my time trying to deliver a package if one was loose in someone's front yard. Bad choice.
Consider insuring your packages. Otherwise they (Fedex) are only responsible up to $100 for replacement value. Fedex can give you rates (1-800-GOFEDEX or 1-800-463-3339). Get after them ASAP if you have a damaged package, otherwise they'll leave it up to you and your supplier to sort out.
I have plenty of bad stories, worst of which involved two coolers of environmental samples worth $30,000 (cost to repeat test project), which were lost in transit and never found. Guy who shipped them had insured them but Fedex said they would only cover the cost of analysis, not the labor to collect them again. So we lost $27,000 and had to repeat the effort on our dime.
I believe they have a big graveyard down in Memphis if I understood them correctly full of lost packages where packages with labels missing are sent. Probably what happened to mine.