J.C. Penney (NYSE:JCP) has a tiny sliver of hope.

The struggling retailer recorded a slight profit in the fourth quarter despite reporting a 7% drop in comparable-store sales. J.C. Penney had a net income of $0.08 per share and finished the year with $1.8 billion in liquidity.

The exterior of a J.C. Penney

J.C. Penney had a better-than-expected quarter. Image source: J.C. Penney.

Doing it right?

CEO Jill Soltau faces a nearly impossible task. She has to radically remake her chain's stores while also preserving cash. In Q4 she managed to cut inventory and increase profitability even though sales dropped by 7.7% to $3.38 billion, compared to $3.67 billion for the fourth quarter last year.

"I am encouraged by our progress, especially in our women's apparel businesses," she said in a press release. "We knew it would take time to restore discipline and return growth to JCPenney."

Can J.C. Penney recover?

The challenge Soltau faces is that you can't cut your way to success. J.C. Penney may have bought itself some more runway but not going out of business is not really the measure of long-term success.

Soltau needs to make massive investments in the chain's dated stores. She also needs money for inventory and to invest in her company's supply chain and digital experience.

It may be possible to make those changes slowly if the CEO can keep the ship afloat. The problem with moving slowly, however, is that the destination can change before you have even finished making your moves.

J.C. Penney remains on life support, but its CEO does deserve credit for keeping it alive and giving it at least a chance of a miracle comeback.