You can definitely chamber and fire 44-40 and 303 in a .410 gun, but whether or not it's actually a good idea, is something else entirely. .45 Long Colt will also chamber and fire.
As for safety, I wouldn't do it with either 44-40 or 45 Long Colt. The chamber pressure is going to be significantly higher than the gun is designed for, and although if you're using soft lead boolits, they should swage down through the choke, you're asking a lot from the barrel. It's been done, and people have gotten away with it, but I wouldn't call it a good idea.
Although .303 has a lot more power behind it, it's actually safer. Because the bullet diameter is so much less than the barrel, any over-pressure just escapes around the bullet. The accuracy will be non-existent, as the bullet rattles its way down the oversized barrel, and you won't get much velocity either, as so much force is lost with the gas escaping around the bullet. It falls into the category of "stupid party trick" - not smart, not useful, waste of ammo.
You can use the brass from the above cartridges to make .410 brass, though. I don't use 44-40 or 45 LC, because you end up with quite a short cartridge with limited capacity. However, carefully fireformed .303 brass works out to slightly more than 2.5" case length, which is the same capacity as a 2&3/4" .410 shotshell (the length is measured after the crimp has expanded out - 2&34" .410 shells only have 2.5" capacity, give or take a few mil.)
I use these for varminting, because at close to 1$/shell for commercial #6 loads, it seems a bit pricey for blasting gophers at close range. I H110 powder (look up your own load data, and go with what you feel safe with), a cotton wad cut from cotton cleaning patches, plastic shotcup wad (cheap bulk), 1/2oz of #6 shot, and then seal it with about 1/4 of a cotton ball wetted with Elmer's glue. With a primer, my cost works out to around 12 cents a round. Unlike plastic hulls, you can reload the brass virtually indefinitely.
Effective on gophers at 15 yards without any issue, 20 yards on the "extreme". I could probably push that if I mucked about with my powder charge and shot size, but that covers what I want it to do (gopher shots at 10-15 yards, which is a bit close to try and get a scope on with my .22).
Also, they look spiffy.