When mapping reads to a reference genome, what you would have is a consensus, not an assembly. This would be a reference with variants introduced from your mapping data. If you mean to say that assembly of the reads which map to a genome is fragmented, it is due to the uneven coverage, genome complexity and repeats. There are approaches to make local assemblies out of mapped reads, which work to an extent.

You can do both reference-guided as well as denovo genome assembly.