In a Sanger sequencing, what would be happen if different DNA sequence binds to same primer? And how this situation avoided if problematic?
Yes, this can happen if you are not checking your primers against the reference sequences.
Your PCR is done from two different pieces of DNA leading to two sets of chain-terminated fluorescence marked DNA. This leads to superimposed sequences, which looks like this and where you cannot differentiate, which sequence belongs to which strain (image taken from here):





It is problematic, the solution is to design new primers (which are located slightly outside the old target sequence) which only bind to one specific sequence. You cannot purify only one product, as you cannot discriminate between the two.