This paradox occurs when objects because of time travel actually have no origin. No beginning. There are a couple of variants. The first is the reverse grandfather paradox, where instead of the time traveller going back in time and killing his grandfather, he has intimate relations with his grandmother and ends up becoming his own grandfather. Fry from Futurama did this after accidentally killing off the man he always believed was his grandfather, in essence meaning that when he was born he actually had no grandfather. (I have to admit I quite like Futurama.)
But the concept is probably best seen in the movie - "Somewhere in Time." Christopher Reeves meets an old lady somewhere in the future, and she gives him a watch. He then goes back in time and meets her as a younger woman, and gives her back the watch, so that she can then complete the cycle and give it to him when she's older again.
Now the heart of the paradox here can best be understood if you ask yourself one question, how old is that watch? The answer is that there is no answer. There can be no answer. As far as can be determined the watch never began. It simply arrived at some point in time and then kept re-arriving there. So from some perspectives the watch may be ageless, it may also be all ages at the same time, and from other perspectives it could actually be infinitely old. After all if you stop at any point along the time continuum during the period when the watch is in either character's hands, you have no idea how many times its been through that cycle - old lady to young man to young lady to old lady to young man etc.
There are of course more violations of physics than just this occuring. For a start the watch is not aging as it goes through the cycle. If it was, even very very slowly, the watch would eventually turn to dust, and the old lady would have nothing to give the young man. But of course that would also mean she could never have received it as a young woman and the paradox / cycle could never have begun.
So the watch has to somehow be unaffected by time. But more than that it has to be completely unaffected by everything. So if the woman became angry one day and threw it at the wall, it might chip the wall but could never in turn be chipped by it. Because if it were, then with every repeat of the cycle that chip would become worse. Theoretically therefore the watch actually must be indestructible.
And of course if the watch was a wind up type, the coil could never be overwound so as to damage the watch and stop it working.
I wonder how much someone would charge for a watch like that? (Though of course the watch could never be sold since it has to be back in the old lady's hands later on to give to Christopher Reeves. - Maybe you could borrow it though?)