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In order to be eligible for benefits, a claimant must be unemployed "through no fault of their own." If you are being let go but your employer is offering you another position, the issue will become whether you have refused an offer of "suitable work." If the unemployment office finds that you have, you will be denied benefits on the ground that you are unemployed through fault of your own--that is, you were made an offer of suitable work and you refused in favor of being unemployed.
Whether an offer of work is "suitable" will depend on a number of factors including comparability to the employee's previous position in terms of pay, responsibility and opportunity for advancement. It will also take into account such things as commute. However, 20 miles away probably would not be so far that an offer of work would be considered "unsuitable" on that basis alone.
Ultimately, there is a question of fact here, meaning the unemployment office examines the unique facts of each case and makes a determination based on the specific circumstances. The issue boils down to whether a person genuinely desireous of being employed would have turned down the offer. If you can prove that to be the case here--meaning the job is substantially lower pay, or responsibility, or there is some other factor which makes it much less desirable--then you will be able to collect benefits. But due to the uncertainty of being awarded benefits under these circumstances, it is generally better to accept the new job and simply start looking for other work, then quit only once you've secured a better offer of employment somewhere else.
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