Dorsey told CNBC on Friday morning that he believed in the company's current plans. Markets showed muted enthusiasm for the changes Friday. Twitter stock closed just 0.2 percent higher at $35.90
Read MoreDorsey: 'I believe in' Twitter's strategy
For Seaburg, who has taken a short interest in Twitter, a lack of change means the stock could fall even more. He contended that shares could fall below $30.
While investors showed little hope for Twitter on Friday, trader Guy Adami feels the company can turn itself around.
"I do think they can figure this out," Adami said.
Read MoreAfter CEO exit, Twitter says no strategy change
If investors buy the stock, they should use $35 as a stopping point, he said. Trader Brian Kelly agreed that investors may want to buy Twitter at its current levels.
While trader Tim Seymour did not think the stock makes a strong investment, he said he would rather make a trade on the long side than short.
Tim Seymour is long AAPL, T, BAC, C, DIS, F, GE, GM, GOOGL, INTC and SUNE. Tim's firm is long BABA, BIDU, MCD, NKE, NOK, SBUX and YHOO.
Brian Kelly is long DXGE, BTC=, BBRY and U.S. dollar. He is short Australian dollar, Canadian Dollar, euro, yen and yuan.
Guy Adami is long CELG, EXAS and INTC. Guy Adami's wife, Linda Snow, works at Merck.