Some fear the company, Europe's largest independent oil refiner, may close one of its plants as it struggles to secure funds to maintain its operations.
The spotlight has fallen on Petit-Couronne in Normandy, France, and Switzerland's Cressier refinery in the Neuchatel canton, reportedly the least profitable in the last quarter.
The French goverment has assured French unions that it is pulling out all the stops to assist Petroplus during its ongoing talks with lenders.
Yves Scornet of the CGT said on Thursday that workers feared any partial restoring of credit would see funds channelled to the Coryton refinery in England and the Petroplus plant in Ingolstadt, Germany.
Scornet added however: "The government has assured us that there will be no solution that does not include the French refinery."
Neuchatel authorities said they were in daily contact with management at the Cressier refinery where 250 people are employed.
"The situation is serious, but not catastrophic," the region's economy minister Thierry Grosjean told the ATS news agency.
Grosjean said the most likely scenario was that Petroplus would close one of its refineries, but not necessarily Cressier.
The refinery may be spared due to its small size, treating about 68,000 barrels a day, and it is one of only two refineries in Switzerland, the official said.
Current stocks will last for about three weeks, he added, with all sides determined to find a solution.
The Cressier refinery, opened by Shell in 1966 and run by Petroplus since 2000, produces about a quarter of the total refined products sold in Switzerland.
Petroplus announced on Tuesday that its lenders had frozen $1 billion in uncommitted credit lines -- funds it said were "critical" for it to continue its operations.
The news sent shares on the Swiss market tumbling and on Thursday credit ratings agencies Standard and Poor's and Moody's slashed the firm's rating, indicating it was vulnerable to default.
Petroplus Holdings AG is headquartered in the city of Zug near Zurich and headed by Frenchman Jean-Paul Vettier.
The company had discussed with lenders options to "reduce their risk", spokesman Fredrik Olsson said following the announcement, but a request for more time was not granted.
Petroplus has not issued any statements since and could not be contacted for comment.
The group, which employs 2,500 people, indicated at the beginning of December that it faced increasing liquidity problems.
Its five refineries, which include the Antwerp plant in Belgium, have a combined capacity of about 667,000 barrels a day.