Act when the employment end date becomes known. Ask counsel to identify the applicable deadline using the termination terms, admission record and grace-period rules. Leave time to obtain documents and compare an eligible filing with departure; neither an employer discussion nor a proposed offer extends the deadline.
Work backwards from the last day of duties
Set the departure or filing target from the actual end of professional activity, not from the record's expiry date. If a new employer is interested, ask counsel immediately what sequence that route requires and whether the person must be outside the United States for part of it. Leaving the question until the final week narrows the available options considerably.
When two calendars compete, the one that governs is the end of professional activity, not the project schedule and not the printed expiry on the record. Put the known dates on a single line, being the last day of duties, the admission validity and any prior use of a grace period within the current authorized validity period, and the available window becomes visible without guesswork. The usual failure is a slow start followed by a rushed choice: weeks spent waiting for an employer to confirm something informally, then a single week in which documents, a filing decision and travel all have to happen at once.
Fix the earliest date on which the person would have to leave if nothing else changed, and treat every other option as something that must be arranged before that date.