If I may ask, which weight lifting exercise caused the problem?
I don't know which lift the author was performing (and would ask you not to repeat it if you do know), but of the popular lifts which could cause a problem if you fail:
1) Bench press. Have a spotter or don't use clips (the things that hold the weights on the bar). Some benches will have safety bars which can help as well. If you don't have clips you can tip to one side and dump the weight off the end of one bar, then the bar should roll of you (albeit painfully/noisily). People have died benching alone in a gym, don't get caught out.
2) Squat. Have spotters and/or squat in a cage/safety rack (with parallel bars either side of you). It can be dangerous if you fail, have no spotters and aren't in a safety rack. i.e. you can dump it, but this can be dangerous to you and those around you.
Stay safe everyone.
But naturally by virtue of not increasing the weight on the bar one will reach a point where one ceases to get stronger (measured by the amount of force you can produce). There are limits to what more reps will do for you.
So don't deadlift your 1RM every time you go to the gym, just slowly increase how much you lift in a safe and structured manner.
So unless you are a professional (then you already know about this more than I do), lower the weight and stick rather with 15-20 reps. If you feel that given excercise is too easy during set, just another 5 reps and try to do perfect movements. YOu can get the same famous 'burn' in the muscles. This also builds stamina, which is much more beneficial in real life compared to pure power for few seconds.
Needless to say, since I switched, i didn't have a single injury, not even minor stretches. Even if I am totally exhausted, I can handle the loads I use to put them down/to the rack safely.
If you want to just train, go for the safe options and a bit more reps. If you want to really break your limits, never not have a spotter. They will allow you to be a bit less safe on the one hand (e.g. bars with max weights) and provide you with motivation on the other. I never pushed past my limits before I had a spotter.