The family of bankrupt businessman Seán Quinn will ask the High Court to lift orders freezing their accounts and preventing asset transfers in the International Property Group.
The Quinns claim the insolvency of Irish Bank Resolution Corporation means the orders freezing their accounts below €50m should be lifted urgently.
They say the bank's undertaking for damages on foot of which it got those orders is now "valueless".
Alternatively, the Quinns say the special liquidators of IBRC must lodge up to $500m dollars in court to meet any claim for damages should they win the case.
Mr Justice Peter Kelly said the matter was urgent and he would hear it next Monday.
The price of an injunction is an undertaking for damages from the party seeking that injunction and it would be wrong to permit a "worthless" or "hollow" undertaking from an insolvent entity, he said.
In a sworn statement, Aoife Quinn said it was clear from recent remarks by IBRC special liquidator Kieran Wallace that any claim the Quinns may have on foot of the bank's undertakings for damages will rank as "an unsecured debt which Anglo will be unable to satisfy".
The freezing orders have caused considerable loss to her family and it is "no longer just, equitable or conscionable" that they remain in place, she said.
The orders had led to termination of standing orders and direct debits on the accounts of herself, her siblings and other family members which had led to non-payment of a range of expenses.
The "most striking example" was that mortgage payments on Seán Quinn Jnr's home were not paid, despite the fact the account from which those payments was to be made was in credit, she said.
KBC bank had appointed a receiver over that property, she added.
They were also unable to contemplate new business ventures or employment, to maintain ordinary banking facilities and were delayed in getting the full legal advice necessary, Ms Quinn said.
The family claims the appointment earlier this month of special liquidators to IBRC, formerly Anglo Irish Bank, means it cannot honour its undertaking to pay them damages should it lose its case against them over alleged stripping of $455m assets from the IPG.
Therefore, they claim, the bank is not entitled to various orders obtained so far in its case, including orders of July 2011 restraining them transferring IPG assets and orders of July 2012 appointing receivers over their personal accounts and assets.
When Martin Hayden SC, for the Quinns, moved the family's application today, Shane Murphy SC, for IBRC, said he needed an opportunity to take instructions from the special liquidators on the issues raised.