This article suggests that with the declared bankruptcy, and subsequent closing, of Chrysler, other auto manufacturers might have to face shutting down as well. This is because the plants in charge of supplying Chrysler with parts will suddenly be losing a lot of money, possibly closing down, leading to a shortage in parts in the auto industry.
Looking at the situation as if the car manufacturers are in monopolistic competition, it can easily be seen that one firm leaving the industry could allow other firms to increase production, possibly even bringing them out on top of this economic recession. However, the article is right to look at the parts manufacturers.
Parts manufacturers, with the exit of Chrysler, suddenly find themselves with a decreased demand for their product. Again using the monopolistic competition model, this would result in a sharp decrease in quantity produced, with an increase in price. This demand shift occurs due to two reasons: first, the firms that produced Chrysler-specific parts no longer have any sellers; second, the firms had already been giving the auto manufacturers as many parts as they needed.
With the price increase on one of their inputs, auto manufacturers may find it difficult to continue production at current levels, at least as far as the short run. Lowering production means lowering already low profits, which could force auto manufacturers to close plants or even declare bankruptcy themselves.
It is possible that the closing of Chrysler would increase demand for other types of vehicles, because people who would have bought a Chrysler would eventually no longer be able to do so. But Chryslers aren't going to simply disappear overnight, and a manufacturer declaring bankruptcy could shake consumer confidence in all auto manufacturers, decreasing demand even further. It's difficult to say which shift will be observed until it actually occurs.