"I'm not walking away," said Wrathall. "I've got too much invested in this club to just walk away and have a clean sweep.
"We've got a lot of creditors and we are going to stay and pay them."
Wrathall and Stapleton own 49% of the shares in Plymouth Argyle along with Robert Dennerly, while the remaining 51% is shared between Japanese businessman Yasuaki Kagami (38%) and Sir Roy Gardner and Keith Todd (13%).
Argyle are currently bottom of the League One standings having been docked 10 points on Monday after issuing a notice of intention to appoint an administrator.
The notice is classed as an insolvency event which breaks Football League sanctions and results in the automatic 10-point penalty.
Plymouth's football consultant Peter Ridsdale is leading the search for new investors at Home Park having previously told the BBC that £2m is needed to ensure the club survives until the end of the season.
On Friday, Ridsdale told BBC Spotlight: "We have three buyers who we think are very interested, two of whom are slightly further ahead than the third.
"There is a strong possibility that prior to a final conclusion we may well have to go into administration."
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