In UDP, instead of waiting for a dropped packet to be resent again, you can just make 100 copies of the same packet and send them all in case some of them are dropped. You kind of flood the network a little bit, but it's faster than the TCP way of handling dropped packets, which is what is needed in FPS games.
That's a bad idea. First, you would increase the bandwidth by two orders of magnitudes, which is not just a little bit. Second, today the majority of packet drops are caused by congestion, meaning that not just one but many packets are dropped, so if you send many at the same time you still risk losing them all.
Back to the original question, your solution is to not only send position but also velocity (and possibly acceleration, depending on the game), as well as a timestamp. On the other end you will then be able to calculate the expected position at any time from the last known values of these parameters. You can improve this further by using various techniques for interpolation and clock synchronization.