Something like this happened in 2008 with Volkswagen and in the process caused that company for one day to become the most valuable in the world as all the short sellers, upon discovering their predicament scrambled to try to cover their positions.
At the time Porsche was known to have been buying shares and had acquired a 35% stake in Volkswagen, the state of Lower Saxony was another major shareholder, owning 20%. Once Porsche reached 30% ownership it was required to make an offer for the whole company but that offer had been rejected by the other shareholders.
Short sellers looked at the shares and found that preference shares in Volkswagen that had no voting rights were worth much less than ordinary shares that had voting rights. A number decided to try to take advantage of that price gap since ultimately preference shares conferred the same ownership rights over the company and its dividends. The gap had been caused by Porsche buying only ordinary shares as they had needed the votes when they bid to takeover the company.
The short sellers managed to short 12% of Volkswagen. At this point Porsche disclosed that they had increased their holding of Volkswagen to 42.6% and in addition had also bought options on 31.5% of the remaining shares. This meant that between them Porsche and the state of Lower Saxony owned (or would own when the options settled) 94.1% of Volkswagen. The problem for the short sellers was immediately apparent as they needed to buy back 12% of Volkswagen in order to unwind the shorts when only 5.9% was available. The share price increased fivefold as the shorters scrambled to buy that 5.9%.
Eventually Porsche sold around 5% of the company so the short sellers were able to settle albeit only after racking up $20 billion in losses. Porsche on the other hand had a huge option bill to settle, which nearly bankrupted it.
So although Porsche never owned more than 100% of Volkswagen they and the short sellers did sum to more than 100% in a sense.
This was covered by many news sources if you want to read more about it