To answer the OP, yes, some people have put forward theories in which Jesus did not die on the cross. The people behind The Holy Blood and the Holy Grail suggest that Jesus survived and even had children. Barbara Thiering has written several books arguing that the Gospels should not be interpreted literally, but as allegorical texts known as ‘peshers’. Google will find you more.
Whether he actually did or not is something we do not know and cannot know. We have no way of determining that particular point.
Try this little thought experiment. Imagine an event which took place within the last 40 or 50 years i.e. in the modern age of mass media, with a large crowd watching from all sides, with a colour film recording everything, with someone else making an audio recording of everything, and in broad daylight with clear visibility. You’d think we could be pretty sure about the details of that event, right? Well, not if it’s the assassination of JFK. Sure, most people either don’t know much about it or figure that it was just LHO on his own, but just look at the endless list of books, videos, magazine articles and, indeed, formal legal cases, that disagree about what hapened. And we can’t definitively prove it one way or the other.
Now contrast this with an event that took place roughly two thousand years ago (i.e. longer than you can even imagine), before any modern media, with no film or video, no audio record, not even someone on hand to make a sketch or painting, in a foreign country most Westerners couldn’t even find on a globe, and of which the first written account was written at least 70-90 years after the alleged event took place (and that’s a conservative estimate). What’s more, that first written account has been re-copied endless times, translated and re-translated and re-interpreted endless times for over 1900 years - sometimes by peope with a vested interest in making it say one thing and not another - before it gets to you, from a language which doesn’t use the same alphabet or grammar as English, and from a time in history when only specialist historians can agree what words meant (is that ‘virgin’ or ‘young woman’ or ‘betrothed young woman’?). You see the problem? The fact is, we don’t know what happened and can’t know. People who claim otherwise are being fanciful in the extreme.
Be clear: faith is not knowledge. If it were, it would be based on facts and evidence. As such, any ‘faith’ has the same truth value as any other. If you want to believe he died on the cross, that’s a perfectly good faith. If you want to believe he didn’t, that’s just as good a faith. If you want to believe he was never crucified at all, that’s just as good too.
I don’t know if Jesus died on a cross. I do know that throughout history lots of people who believe one version of events have seen fit to fight, kill and slaughter people who believe a different version of events, spilling a lot of innocent blood in the process. In other words, if Jesus did die on a cross for any purpose, that purpose is often served least well by those who claim to act in his name. And that is a fact.