How does a TDM multiplexer "catch" all bits?
In my opinion, you are missing the simple input buffers. Let’s consider the traditional PDH system. A 4-1 multiplexer tries to construct an E4 signal from the 4 input E1 signals. All inputs must have buffers long enough to be able to tolerate the problem you mentioned. Apart from that, there is no guarantee that all inputs will have the same exact clock. What happens if input B has 999 bits when is was supposed to have 1000 bits in the buffer? This is where bit stuffing and rubbing help. These problems are solved using control bits in the next generation SDH systems. So basically, 2 standard TDM transmission systems solve the problem you mentioned by buffering + control bits (pointers).