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401(k)s and other qualified plans are owned by specific individuals. If your spouse becomes "totally and permanently disabled", your spouse can withdraw from your spouse's plan without paying the penalty. However, you still pay the penalty if you withdraw from your plan before age 59-1/2, even if the reason you made the withdrawal was the disability of your spouse.
Also, "totally and permanently disabled" means unable to perform gainful work due to a condition that is permanent or will lead to death or is expected to last at least one year. Gainful work is anything you can do to earn a living. Many people who have medical disabilities (blindness or amputation, to give two possibilities) can still perform gainful work, so would not meet the IRS standard.
If you claim a disability exception to the 10% penalty on your tax return, you don't send proof to the IRS with your tax return, but keep your proof for at least 6 years in case of audit.
Remember that even if you qualify for the exception to the early withdrawal penalty, you still pay regular income tax on any withdrawals of traditional/pre-tax retirement accounts.