I guess I'll field this one, now that Shoemaker has officially been DFA'd.
Shoemaker's leash in the pen was indeed pretty short -- first relief appearance was on June 11, and last on June 30. That's less than 3 weeks. Only 3 consequential appearances, really -- the controversial first one, an effective extra innings win vs Cincinnati on June 21, and last night. I think if he had struggled vs Cincinnati, he probably would have been cut 10 days ago, which would have been one week and change in the pen. As it happened, he looked good in Cincinnati, and bought himself one more try, in which he epically failed last night.
As far as replacements, while Shoemaker has been in the pen, we've lost Pineda, Dobnak, Farrell, and Duran to the IL, joining Stashak (recently moved to the 60-day IL), Smeltzer, Colina, and Thorpe. (Maeda, Thielbar, and Shaun Anderson were also on the IL at the start of Shoemaker's pen assignment, but have since been activated.)
We've already had Jax and Coulombe on the 26-man roster, and ahead of Shoemaker on the pecking order; now Derek Law is returning to take Shoemaker's place. It's not a deep group at the moment. (And the point of claiming Burrows was that he has minor league options remaining, not to place him back on a MLB roster immediately.)
None of this should be read as a general defense of the front office or field staff -- the Shoemaker acquisition was indeed disastrous, and the lack of viable replacements ultimately comes down on them too. But the leash itself wasn't particularly long or problematic.