Industry website Demolition News said the firm was now in the hands of local liquidation specialists French Duncan.
Border was based in Glasgow and had been trading since 1997 when it was set up by founder Peter Beattie who has nearly 30 years experience in the demolition business.
The firm was a National Federation of Demolition Contractors member and had worked on a series of high-profile projects including Gleneagles Hotel and the Royal Bank of Scotland headquarters in Edinburgh.