When employment ends abruptly or when it's not your fault, it's more likely that you'll qualify for unemployment benefits. Each state has procedures in place in order to determine eligibility when opening a new claim. The same is true for reopening a claim. Depending on state regulations, an existing claim may be reopened if you become unemployed again or a new claim may need to be filed.
If you are furloughed or laid off again, you may be eligible to reopen your unemployment claim. This may be possible if you worked part of the week but some states require a full week without work in order obtain benefits.
Working full-time may not make you eligible for benefits but working part-time or having reduced hours may make you eligible to reopen an existing claim. This may result in filing for a partial unemployment payment with a one-week waiting period but it depends on the guidelines of your state and whether or not unemployment can be paid.
If you are fired from employment, usually it's unlikely to qualify for unemployment but depending on the reason for leaving, you may be able to reopen a previous claim. However, in many states, a waiting period may apply.
There may be other reasons for leaving employment in requesting to reopen a previous claim that should be reviewed with the unemployment agency when reapplying. If you obtained a job with another employer but working conditions were considered unsafe, you may be able to reopen an existing unemployment claim. You may have to provide proof of your claim upon reopening.