In both the United States and Mexico, there are federal institutions that protect the savings accounts of the banked population.
In Mexico your savings are protected by the Institute for the Protection of Bank Savings (IPAB). Instituto para la Protección al Ahorro Bancario (IPAB). If a natural or legal person opens a savings account in any bank, the IPAB covers up to the equivalent of 400 thousand Investment Units (UDIS), that is, approximately 2 million 55 thousand pesos, this for each bank, that is, it is possible have different accounts that do not exceed that amount.
In the United States, on the other hand, there is the Federal Deposit Insurance Corporation, an independent federal agency, which guarantees the recovery of money to users if a bank fails and stops operating. The FDIC protects all deposits of amounts less than $ 250,000.
If you have your savings in Mexico and you are looking to transfer it to an account in the United States, you can make an international transfer. The options are bank transfers, which depend on each bank; through money transfer agencies; or through internet payment systems.
Remember that most banks require at least your official photo ID and the taxpayer's personal identification number (ITIN), in order to open an account in your name.
CONDUSEF
https://www.condusef.gob.mx/index.php/comunicados-de-prensa/Revista/?p=contenido&idc=837&idcat=1
LA SILLA ROTA
https://lasillarota.com/dinero/que-pasa-con-mis-ahorros-si-vivo-en-estados-unidos-/532573
JUST LANDED
https://www.justlanded.com/espanol/Estados-Unidos/Guia-Estados-Unidos/Finanzas/Transferencias