Can a company lay you off and then offer you a job back at a lower pay?

Yes, they can, as long as it does not violate other rights and agreement under the law.  The first situation I can think of would be an employment contract you have with the employer.  It also can not violate any discrimination laws (like your age). And they can not fire you to get back at you for having filed a claim against them - like an OSHA violation for safety - or for using a benefit under the law (like FMLA leave).  Good luck.