For unemployment purposes, I think you could safely assume that "suspended indefinitely" is sort of code for "fired." He can file a claim during the first week he is actually not working. Even if he is put out of work and the company says they indended to put him back to work at the time this "indefinite" suspension was over, he is still able and may be eligible to receive benefits. Because during this time he is out of work not by his choice, (if so determined.)
But if this person was in someone's home working on their television, he might in many cases be a contractor instead of a regular employee. If so, then he's not got any case for filing for unemployment insurance against this employer, as he has been working as a contractor. Whether he gets to set up a claim, based on monetary eligibility would be from the last 18 mo to 2yrs, wages made from covered employers. Then the reason for leaving would be from the last covered employer he has worked for.
If that covered employer is the one who has indefinitely suspended him, then they would be asked to give the reason for his "suspension," and if they were not determined to have a good misconduct reason for termination, he would be able to be approved for benefits.