Bright Property Agents, in Strathaven, South Lanarkshire, was run by husband and wife Alan, 34, and Jennifer McIntyre.
It is understood the couple have gone to the United States where 35-year-old Jennifer originally comes from.
Customers who rented properties from the firm have been left fearing they have little chance of being given back their deposits.
A solicitor's office near Bright's base has been inundated by worried locals who have been unable to get in touch with the couple.
Euan Stirrat, senior partner at Jackson Dick Law, said: "We knew nothing about Bright's closure and had never dealt with them directly, but are doing everything we can to help landlords and tenants who have been affected."
Legislation came into effect on November 13 which requires letting agents to keep customers' deposits in a separate, secure account.
Bright's office was open as normal on Wednesday, November 14, but was empty and abandoned the next morning. The firm said in a letter sent to landlords and tenants last week it was in the process of nominating a liquidator.
It added: "No one is more disappointed than ourselves that we have had to make this very difficult decision."
Managing director Ian Potter of the Association of Residential Letting Agents – of which Bright was not a member – said that all ARLA agents must adhere to a strict code of conduct.