Even if the wing was broken, which it might be, there is no way to know without an X-Ray, they still would only wrap it against his body to keep it from moving around, that's all you could do anyway...
***The average lifespan of a Budgie IN CAPTIVITY is NOT even close to 5-8 years!!! That's a common misconception (unfortunately), and it's also the reason why people buy them for their young kids, thinking of them as a "throw-away" bird or a "starter bird", when in reality Budgies are every bit the Parrot as a Cockatiel, a Conure, an Amazon, etc. are. It's important that false-information about their average lifespan is corrected, so please don't think it's only 5-8 years, even with sub-par care.
***Budgies and Cockatiels have similar lifespans, with the average lifespan in captivity (as pets) being into the mid to late teens, with the average being around 14-15 years. My first Budgie lived to be 18 years and 9 months (I got him when I was only 6 years-old and he went away to college with me!), and he was actually fed a regular, daily staple diet of a healthy seed-mix, along with a daily portion of fresh veggies and dark, leafy greens. He also had a weekly Honey-Stick as his only treat (no millet sprays). So I didn't do anything special, he wasn't even fed pellets as his staple-diet, and he lived to be almost 19. He did get a good amount of out-of-cage time every day with me and got to fly around a room with a closed door for a good couple of hours each day.
The bottom-line is that there is no reason at all that any Budgie in captivity shouldn't easily live to be around 15 years-old, usually older than that (The record lifespan for a Budgie in captivity is 29 years-old BTW)...The keys to a long life of ANY PARROT of ANY SPECIES is #1) A healthy daily diet that is low in fat and high in protein (avoid dried Corn, Sunflower Seeds, and all Nuts except as very occasional treats), and is varied, meaning they should get a daily "staple" food of either a low-fat seed-mix meant for Budgies, or an Avian pellet diet, or a mix of both, along with at least one serving for fresh veggies and dark, leafy greens every single day, with little Fruit due to the sugar content...#2)They need to be treated the same as ANY PARROT does, meaning they need out-of-cage-time of at least a few hours every day, and even though you already got their wings clipped, it would be in their best interest that after you earn their trust and get them hand-tamed/trained to step-up for you and come to you on a regular basis, that you allow their wings to grow in fully so that they can get exercise each day by being able to fly around a safe room with the door shut every day...and then #3) Just giving them as much of your time, attention, and love as you possibly can each day...
A lot of people commonly treat Budgies more like furniture than they do a pet parrot...Unfortunately this is devestating to they physical and psychological health, as Budgies have the intelligence of a 2-3 year-old human child, just like any other species of parrot. They are simply smaller in size than other parrots. That's it, that's the difference.
And while their lifespan in the wild is very low, around the 5-8 years that someone listed above due to their small size making them an easy target to predators in the wild, in captivity as pets they don't have these issues, and if given ample attention, interaction, love, and if they are treated the same as you would treat any other parrot species like a Conure, Amazon, etc., they will not only learn to do the same things that the larger parrots do, such as stepping-up, flying to you on command, talking with a huge vocabulary, learning tricks, etc., but they will also live to their full captive lifespan easily, which should be around 14-15 years or longer...
