In which sequencing technology the read can Not exceed the fragment length?
I would say that the question is not all that well defined.
When a read runs into the adapter, it does not mean that the read is "longer" than the DNA fragment.
It means that the instrument ended up sequencing the region of the DNA fragment that has been artificially added to the end of another, shorter sequence.
In theory Sanger/PacBio/Nanopore would be able to keep sequencing the entire length of the fragment if polymerase/reagents keep doing their work without any degradation. Nanopore reads can be megabases long (not sure what the current record is).
With Illumina largest sequencing kits you get are for 600 cycles (so other than the caveat mentioned by @Istvan and if your insert size is > 600 bp) you can at most get 600 bases (+ 10-20 at most) before you simply run out of sequencing reagents. So with Illumina a single read can't be longer than ~ 620 bp at most (assuming you set the sequencer up to just keep going with read 1).
I think I might also not fully grasp the question.
There is no sequencing technology for which the read can exceed the fragment length (given that the fragment is the template for all of those techniques). None of them can 'invent' sequence that is not there.
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version 2.3.6
purely technically speaking the Illumina sequencer could do that - I believe once it runs out of everything: sequence + adapter, etc it will start producing As - until the read-length is reached.
Illumina sequencing machines don't always add "A". I saw more or less random sequences after the adapter. I wasn't able to understand how Illumina software decides which random sequence to produce after the adapter. Also, in Nanopore sequencing the length of the read is not equal to the length of the fragment, because by "fragments" people usually mean the fragment of the target genome, while Nanopore also sequences adapters. I didn't have much experience with PacBio, but I suppose that it sequences adapters too.
I see , but then also Sanger should be able to do this, no?
Likely pacbio & nanopore not as the first needs a polymerase to function (and no template no polymerase activity) and the latter 'reads' the electric signal (so no 'template' no signal anymore)