Well, not indefinitely, but if they are pursuing assets, a Trustee can keep it open as long as necessary.
There are limits, but in the above case there was a definite starting date for the loan repayment (albeit 3 years after the bankruptcy case was filed) and the rights to receive those payments existed prior to the Chapter 7 case being filed, so the Trustee was well within his/her rights to wait for the payments to begin, and take them directly from the ex-husband.
The key here is that this asset (i.e. the right to receive payments from the ex-husband) existed on the date the bankruptcy case was filed.
A trustee can also wait to see if property values increase after a bankruptcy case is filed, such as for real estate, to see if equity is created above any exemptions. As a practical matter, most Trustees will file paperwork (known as a “no asset report”) stating they have no interest in any of the assets if they don’t believe there will be sufficient value, even after waiting, to benefit the creditors.