There could be few facets to such a resignation.
1. Clause for co-terminus- No issue since with the termination of the project, employee too goes.
2. Employee not covered under any such clause or condition but the co/ org is closing due to any number of reasons. Economic non- viability could just be one such reasons. The best course for the employer is to caution the employee about the likely termination or scaling down of employees vis a vis to time. This should also be part of the employee communication and periodical management briefing so that employees understand the trend of manpower reduction and its need plus also self preparing to look for likely options available. This indeed is a good practice than giving a sudden jolt to the employee by laying him off one morning or leaving a job without relief. Many times, many co. go for closure due to numerous reasons and employee cannot or should not keep dragging his feet over the clause in the offer letter. He was looked after during the good time of co and now its his duty to understand. My exp says that most of the people generally side with the employee, which may not be the right approach all the times and in all cases.
3. Two to three month pre notice was a clause inserted in the offer letter for compliance by both the parties. This should be a happy situation , both for the employer and employee. Contrary to these three situation, there could be industry or organisation specific issues for asking an employee to resign and where more often than not, the employee resorts to appealing to the legal authority. Though at times, employee wins, but sadly only after a long run.
There is a common practice amongst many legal offices to generally support the employee irrespective of the genuineness of the employer's argument and justification. This I have seen for many years. An employee in my co. resigned at his own and found job closed in his new office on the day of his reporting. He came back and we showed him his resignation. He went to the court stating that he was forced to resign verbally. We put all justifiable and were as honest as possible, but the court kept rescheduling date after date.
i can say that irrespective of closing all ends, there will be many situations especially for the employer to get into into avoidable legal tangles due to highhandedness of employees. The best is as an employee, keep your eyes and ears opened and study the business environment. Simultaneously, it is extremely important for the HR guys to judiciously play employee and employer supportive cards well in time.