If the investor died while holding a Conditional Green Card, the spouse can continue and file I-829 application. If the investor died while holding a Permanent Green Card, spouse would retain the Permanent Green Card.
If the principal investor passes while under conditional permanent residence status, the spouse and children may file an I-829 petition. If the principal's death occurs during his/her's Legal Permanent Residence status, the spouse and children will obtain the same status.
This situation is addressed in the regulations at 8 CFR 216.6(a)
(6) Death of entrepreneur and effect on spouse and children. If an entrepreneur dies during the prescribed two-year period of conditional permanent residence, the spouse and children of the entrepreneur will be eligible for removal of conditions if it can be demonstrated that the conditions set forth in paragraph (a)(4) of this section have been met.
The form instructions are under review and will likely be changed and may add further information on this and other issues.
As long as the investment is successful and the jobs have been created the surviving spouse and kids can still get the conditions removed.