Good question.
I'll try to answer it with examples. Let say we have a DNA sequence:
ACGTACGTACGTACGTACGTACGTACGAGACTACGT
Now, for some unknown reason DNA break occurs:
ACGTACGTACGTACGTA | CGTACGTACGAGACTACGT
DNA ends can be joined back:
ACGTACGTACGTACGTACGTACGTACGAGACTACGT
In this example, no evidence of breakage is present.
ACGTACGTACGTACGTATACGTACGTACGTACGAGACTACGT
_________________^----^___________________
In this example, DNA breakage site has additional DNA inserted that is duplicate of one DNA end.
ACGTACGTACGTACGTATTTTTAAAAACCCCGGGCGTACGTACGAGACTACGT
_________________^---------------^___________________
In this example, DNA breakage site has additional DNA inserted and it is unclear were it came from.
This "unclear were it came from" DNA is called "non-template DNA".
DNA end joining mechanism determines such addition of extra DNA in break site (see, http://en.wikipedia.org/wiki/Non-homologous_end_joining).
In breakpoint sequencing there are problems where inserted DNA is longer than reads, because it's hard (maybe even impossible) to map breakpoint.
DNA: ACGTACGTACGTACGTATACGTACGTACGTACGAGACTACGT
# ^^^^^^
Reads: ----------- ----------- ----------- ----------- ----------- -----------
----------- ----------- ------------- ----------- -----------
In this example reads mapped all breakage site (DNA ends + insert): CGTATACGTACGT - now we know that there changes in our DNA and we can still trace back were those changes come from.
DNA: ACGTACGTACGTACGTATTTTTAAAAACCCCGGGCGTACGTACGAGACTACGT
# ^^^^^^^^^^^^^^^^^
Short reads: ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
---- ---- ---- ---- ---- ---- ---- ---- ----
In this example, with such long insertion (that is non-template) it's hard to trace back native DNA site.
Edit
In order to solve this problem Sanger sequencing is used at the guessed breakpoint site.
See figure 4A from http://www.sciencedirect.com/science/article/pii/S0092867411008853 In breakpoint 6 (3105 strand): there is 64bp insertion of non-template (probably) DNA.
Can you provide us with the context of where this sentence comes from? Cancer genome breakage? Is this sentence from this paper -- I don't have access, but Google guides me here. That might help us more.
Yes. That's right.
Here is the full paragraph.
The paper you mentioned is correct :)