A funny thing happened to HP’s TouchPad on the way to oblivion.  It was so successful — now that the company is killing it — that HP has announced it will “produce one last run of TouchPads to meet unfulfilled demand.”

You’ll recall the company said on Aug. 18 that it was getting out of the computer-hardware business.  In the days that followed, it held what amounted to a fire sale.  Retailers dropped the price on their leftover TouchPads to as little as $99.

And all of a sudden HP had a hit on its hands. The TouchPad — which had barely sold in the six weeks since its introduction — became the number-one seller on Amazon.com (for well over $99). Best Buy had trouble keeping it in stock.

“Thank you for enthusiasm for this product,” said HP’s Mark Budgell on the company’s blog, The Next Bench. “Despite announcing an end to manufacturing webOS hardware, we have decided to produce one last run of TouchPads to meet unfulfilled demand. We don’t know exactly when these units will be available or how many we’ll get, and we can’t promise we’ll have enough for everyone. We do know that it will be at least a few weeks before you can purchase.”

Even though Hewlett Packard was the largest-selling computer brand in the U.S., the company decided there was no point in trying to compete anymore in the high-stakes, low-margin business of making hardware. Apple has a lock on high-end computers and handhelds, and companies like Dell and China’s Lenovo have made life tough for HP. So HP announced it would reinvent itself as a software services company, much as IBM did a decade before.

(The tablet market, dominated by the Apple iPad, is still open to new aspirants, if they have deep pockets. The trade media are alive with word that Amazon will start shipping a 7-inch tablet in October, and a 10-inch version in the first quarter of 2012.)

Marlene Somsak of HP was quick to add some qualifiers when we reached her — for instance, that they haven’t set a price for the last-run TouchPads, or decided where they’ll be sold, or whether there will be a limit on how many one person can buy. “This is just a limited run, using leftover parts,” she said. “And it’s just in the U.S. I guess we should have said that.”

It’s actually not such a bad deal for the company. Various analysts estimated that at $99 apiece, HP was probably losing something like $200 on every sale. If, for the first time in its short, unhappy existence, the TouchPad is generating buzz, it can go out on a high note.

Of course, there are naysayers in every crowd. Take the blogger Paul Thurrott. “The TouchPad was worthless when it was fully supported,” he said on PCWorld. “So it’s beyond worthless now.”