How does bit de-stuffing actually work?

So I know how bit stuffing works, it plain and simple you get a bitstream -> 0101101111110, you stuff a zero where there are six 1's and you get -> 01011011111010.

Now while de-stuffing if you find 1111101 in the received bitstream, you change it back to 111111.

But what if the original bitstream had five 1's followed by a 0 and a 1, for example, -> 011111010011111101

while stuffing only the six clumped together 1's will be stuffed with 0 and the bitstream to be sent will be -> 0111110100111110101, but while de-stuffing the output will be ->-> 01111110011111101 which was not the original output. How is this problem solved by computers?