There are specific circumstances in which you can claim a hardship exclusion to the 2 out of 5-year residency rule, in order to receive a partial exclusion of gain, and yes, they involve the timing of the hardship.
There are many facts and circumstances to consider in this scenario. Consider carefully whether you have met the requirements before excluding the gain, and be prepared to present your case in the event of an IRS audit.
Please see IRS Publication 523 for a detailed explanation of the requirements. Here are some relevant excerpts:
Determine whether you meet the residence requirement.
If you owned the home and used it as your residence for at least 24 months of the previous 5 years (leading up to the date of sale), you meet the residence requirement. The 24 months of residence can fall anywhere within the 5-year period, and it doesn't have to be a single block of time. All that is required is a total of 24 months (730 days) of residence during the 5-year period. Unlike the ownership requirement, each spouse must meet the residence requirement individually for a married couple filing jointly to get the full exclusion.
If you were ever away from home,
you need to determine whether that time counts toward your residence requirement. A vacation or other short absence counts as time you lived at home (even if you rented out your home while you were gone).
If you become physically or mentally unable to care for yourself,
and you use the residence as your principal residence for 12 months in the 5 years preceding the sale or exchange, any time you spent living in a care facility (such as a nursing home) counts toward your 2-year residence requirement, so long as the facility has a license from a state or other political entity to care for people with your condition.
If you don't meet the Eligibility Test, you may still qualify for a partial exclusion of gain (see the section Does Your Home Qualify for a Partial Exclusion of Gain?). You can meet the requirements for a partial exclusion if the main reason for your home sale was a change in workplace location, a health issue, or an unforeseeable event.
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