Unemployment benefits are to provide temporary financial payment until you can find suitable work. You have to put forth effort to find new work. The amount of effort varies from state to state. Some states ask that you apply for at least 2 jobs per week or others may ask that you apply for positions that they referred you to. Once you are approved for unemployment benefits, you must make sure that you know what you are required to do for your state, so that you don’t lose your unemployment benefits.
If you fail to accept suitable work, the ramifications are much clearer. The unemployment office will monitor this and your previous employer can even offer you your old job back. Your former employer has an incentive to offer you your job back.
Their tax rate increases when you are approved for unemployment benefits and if you decide not to return to the job, it could be construed as not accepting suitable work since it is the same job.
You can combat this by going back to your old job. It would also make good sense to accept the paycheck and continue looking for a new position. You could also say that your former employer will create a hostile work environment when you return.
Most states allow for you to reject or not apply for work if you can show just cause. There are no guidelines for just cause so it will vary from case to case. You will have to show that any reasonable person would reject this offer of employment or fail to apply. Keep in mind that an employer can contact the Unemployment office and it may be decided that you refused what they deem suitable work for you.