Construction and services firm Carillion said on Monday that it had made an application to the High Court for a compulsory liquidation after failing to secure a rescue deal in talks with lenders and the government.
Lloyds, which was among the banks to stop backing Carillion, said it would provide a £50mln fund for small businesses within the contractor’s supply chain that "may now be experiencing financial difficulty".
The “most severely impacted" customers could receive capital repayment holidays on loans for six months to start with to help with cash flow problems.
"Small businesses don't normally have the cash reserves that larger businesses do, so any interruption to their cashflow can have a significant impact on their ability to survive,” said Jo Harris, Lloyds managing director of business banking.
"By supporting our small business customers during this difficult time, we hope we can help as many businesses as possible to get back on an even keel as quickly as possible."
Lloyds told the BBC it withdrew funding from Carillion because of "viability". "There are reasons the Carillion situation happened,” a spokesman said.
Nationwide said it will take in-house jobs that were performed by Carillion and wants to provide “reassurances" at an "unsettling" time.
The news comes after Business Secretary Greg Clark on Wednesday met with representatives of some of the banks to seek assurances that they would support small businesses affected by Carillion's demise.