The loan company

[Korolina]

The loan company announced it would soon lend money to borrowers with proven records of their not paying back their loans on time, collectively known as the subprime lending market.
(A) of their not paying back their loans on time
(B) of not paying back their loans on time, a group
(C) of not paying back their loans on time, with such a group
(D) that they don't pay back their loans on time
(E) that they don't pay back their loans on time, such a group

[12rk34]

'Their' should be omitted before 'not' in 'A'. What is collectively known as subprime market, is not clear.
'B' is grammatically correct and concise.
'With such a group' is awkward and wordy expression in 'C'.
In 'D' and 'E' placing 'records' before 'that' illogically conveys the meaning as if records don't pay loans on time. 'Such a group' in 'E' is wordy and improper construction.
Hence 'B' is the correct choice.

[Project700Plus]

I go with B as well for the same reason as 12rk34 stated above...

[cartera]

Imo B

The loan company announced it would soon lend money to borrowers with proven records of their not paying back their loans on time, collectively known as the subprime lending market.
(A) of their not paying back their loans on time ---> awkdward
(B) of not paying back their loans on time, a group
(C) of not paying back their loans on time, with such a group ---> the loan company has a group? awkward meaning
(D) that they don't pay back their loans on time borrowers is an object in the sentence, cannot be referred as they, furthermore, collectively know seems to refer to time
(E) that they don't pay back their loans on time, such a group borrowers is an object in the sentence, cannot be referred as they

[mission800]

IMO B
"a group collectively known as" is the correct usage

[Korolina]

Thank you