Hot Topic, where did you find that? Some parts of it are incorrect, at least for my area of the state. If a tenant violates part of his lease the LL can give him a 30 day notice to cure the violation, a 30 day notice to terminate (OH does not force LLs to allow a tenant to cure in all cases), OR a 3 day notice to vacate. If given a 30 day notice to cure, the LL then must issue the 3 day before filing for eviction. If given a 30 day notice to vacate, the LL does not need to then give another 3 day notice prior to filing eviction. (The LL has already told the tenant to vacate and doesn't need to do it again.)
If the tenant does not show up for the eviction hearing, it will be granted to the LL automatically. A magistrate can actually give a tenant more time to move out if the court so wishes. Or they can give as few as 3 days prior to a set out. Here a tag is placed on the door after the eviction hearing saying a set out is imminent. This is the only notice they will receive. The set out can happen within as little as 72 hours of this notice.
The tenant may attempt to contact the LL about the notice. However, LLs here are advised not to speak to tenants after the evictions process has begun, so don't expect a reply. The time to agree not to commit any more violations of the lease was before the eviction was filed with the court. Do this as soon as you receive a 3 day or a 30 day notice. Don't wait until the case has already been filed. Once filed, it automatically goes into the court records, even if later withdrawn. Any future LL will see that it was filed against you.
Finally, to answer CellBoo's question. It depends on why you were evicted from the apt. complex. Sometimes, eviction ends your obligation to pay future rent remaining on your lease. But in some cases it may not. Why were you evicted?