You'd be correct in your assumption: In many of the recent examples we've known about, there's been an auction prior to the implosion, in which everthing from casino and restaurant fixtures and fittings and collectibles to office furniture and supplies were on the block. There's an auction house called Great American Group that generally runs these events, and you can look up the catalog on their website prior to the sale or visit in person at the property during the inspections they hold a day or two in advance.
Most recently, the Tropicana, which is in the midst of a major remodel, held an auction to get rid of old fixtures and fittings. The event took place in San Diego and apparently featured everything from items "from the historic Las Vegas Tropicana Hotel & Casino to general brand-name electronics and general merchandise."
Before it was imploded in July, 2007, the New Frontier auctioned off its contents, as did Nevada Landing earlier that same month, and previously in June. The last auction before these was at the Stardust, back in November 2006, which was a big affair and lasted several days. Lot #1 was announced by former Stardust showgirl Aki, and comprised the crap table that was used for the last throw of dice at the casino on November 1, when the property closed for good. All assets were up for sale, including memorabilia, photos, antiques, playing cards, casino and office equipment, hotel furniture, restaurant and bar interiors, and even the palm trees.
Both the Sands in '96 and the original Aladdin in '98 sold off the contents prior to demolition, with everything from chandeliers and grand pianos to ashtrays and shampoo up for grabs. It doesn't always happen, however. Neither the Castaways ('06), Bourbon Street ('06), nor the Westward Ho ('05) held auctions, althugh the latter did give away a lot to loyal customers who took the initiative to ask.
These days, if a casino closes due to financial problems, the liquidators usually get the booty and if it's simply a matter of changing hands and remodeling -- à la San Remo's transformation into Hooters, for example, the new owners generally keep anything of value that can be re-branded (e.g., gaming tables and slot machines). For example, that huge chandelier in the middle of the Hooters pit may seem a little incongruous, but it was inherited from the San Remo and considered too cool to part with.