What if Chrysler purchased Packard?

When Packard went under Chrysler had three lines. Dodge, Plymouth and Chrysler.. Chrysler was the luxury division of the company. Dodge was the mid-range product and Plymouth was the cheap line.

Chrysler products were designed so that the a top hat could be worn by a man while riding in  one. This single trait no doubt hindered the design of the product line.

After the war Packard acquired Studebaker. Which was to be the lower priced car for Packard. When Packard went under Chrysler was already having troubles. They did not need another luxury level line of cars. It would have expanded the car line to five in number.

What Chrysler did that hurt them so much was hiring Lee Iaocca. While he was good, he made a few mistakes. One was the "K" car. A good concept, but poorly executed. It had dependability issues and signaled the beginning of the end. A series of vehicles followed. All had a similar problem- good idea but poor engineering. The poor engineering was in part due to Lee cutting back on the budget for engineering. Also in part due to the poor choice of Mitsubishi as a partner who provided many of the power trains.

As for Packard, the choice to rebadge Studebakers as Packard was the mistake. Studebakers had a lot of design innovations that were ahead of their time. But cost savings were done in the wrong places. The results were similar to those seen by GM when they rebadged Chevrolets as Oldsmobile's, Buicks and Pontiac cars. Interchange between product lines can only go so far before the public see's through it.

chrysler was struggling themselves in the 50's to stay afloat

Chrysler were owned by Fiat as part of FCA group. FCA has now merged with PSA group to form Stellantis. 

Stellantis owns a luxury brand already, Maserati, so would be very unlikely to wish to purchase a long-dead brand name from the current rights owners (Cooper Industries?) to compete with its own existing luxury marque. They also would not wish to dilute the Maserati name by simply slapping Packard badges on them for sales in North America.

If Chrysler had bought Packard in the past then Packard-Studebaker would not have happened and as Chrysler had a long history of building unreliable turds on wheels, they would have just made Packard-shaped poo instead.

There are many "what ifs" questions you can ask about automotive history alone...

My question would be what if the 4-stroke internal combustion engine had never been invented, what would have taken its place?

It's a strictly hypothetical question because all those events did happen and it shaped the automotive landscape we see today

Mercedes, BMW, and Lexus would have obliterated it a long time ago.

DeSoto and Imperial models have gone.  I doubt if Packard would have lasted.