If you were laid off from a job and you applied to another one if they see that

When I was hiring people, we checked to see if a person was laid off or fired. In most cases, we already knew about layoffs in our line of work, and we often hired those who had been laid off.

There can be different reasons for termination from a job, I am sure employers check into the reasons you give.

Some employers will only confirm dates of employment and not comment on the former worker or why they are no longer employed there

Likely, yes. The ones who don't care are likely lower end places to work

If you have legit reasons for layoff it shouldn't be a problem.