There is a limit and I think it varies:
“In the United States, the National Conference of Commissioners on Uniform State Laws sought to address the problems arising from these types of property through provisions of the Uniform Unclaimed Property Act. The act was first drafted and promulgated in 1981 and a revised version, the Revised Uniform Unclaimed Property Act was introduced in 1995. The act specifically focuses on the problem of unclaimed money in bank accounts and corporate coffers, and the corresponding escheatment.
As a result of the Act, each state that has adopted the act operates an Unclaimed Property fund in which the proceeds from abandoned bank accounts, unpresented checks, etc. are to be turned over to the state after a specified period of time. Depending on state law, the money may be held either in perpetuity (i.e., the funds never escheat to the state; an example would be Texas), or after a long period of time (whereby it is presumed that the owner is deceased with no heirs) the funds will escheat to the state. Due to the increasing mobility of the population, 39 states have joined together to operate ‘MissingMoney dot com’, a searchable database which lists unclaimed funds in these states. Another website at ‘Unclaimed dot org’ allows searches without charge for the remaining 11 states. Many commercial websites also offer this service at a charge. A searchable database for unclaimed money and property is available in Canada from the Bank of Canada.
A similar problem has developed with respect to orphan works, artistic or literary works for which a copyright is in effect, but for whom the copyright owner cannot be found.”
Lifted from Wikipedia