How do you have a viable parish without a minister for four years?
With difficulty. But we know little of their situation with supply priests, deacons etc.
Supply priests, interim pastors, etc. My parish has not had a rector for about 12 months. There are a pool of priests in the Diocese that you can pay to come in on Sundays to run the services. Some are retired, some have secular careers, some have non-parish based ministries (such as the priest that runs the Cathedral Shelter in Chicago).
Of course, that means that there is no full time or part time pastor present to handle the pastoral needs of the parishioners. Lay ministers handle some of this, and some of the supply priests that are local handle some of this. It's not the best solution, but you can keep going if your parish is determined to do so.
If you have a liberal bishop who has to approve the calling, 4 years might be a short time.