The Leeds-based company went into administration with KPMG on 26 February, making around 100 employees redundant.
KPMG kept 22 staff on in order to complete work, while a buyer for the business as a going concern was sought. Only two staff now remain on site and the plant is expected to close at the end of the week.
According to KPMG, its task was made impossible before it was appointed. A spokeswoman said: "We have spoken to a number of interested parties regarding the business and assets.
"Unfortunately, given that the main customers had placed turnover elsewhere prior to our appointment, anybody looking at the opportunity decided against taking discussions any further."
The spokeswoman added that KPMG was looking to sell the assets of the company individually.
Despite the company's predicted closure, there has been some potential positive news for former members of staff.
"We have taken calls from a couple of businesses operating in the same sector asking for details of employees as they have a number of opportunities," the spokeswoman added. "This may enable a number of Blackburns staff to find alternative employment."
Previously a £32m-turnover print and mailing company, John Blackburns went into administration in February 2009. The mailing arm was then sold to the management team a day later.