Losman became the fourth quarterback the team had signed since late July - and the Dolphins' most recent backup quarterback. Sage Rosenfels, who had been Moore's backup, was placed on the Reserve/Non-Football Illness list with an undisclosed illness.
And Moore, of course, had been Henne's backup.
The quarterback situation is even more precarious because of the Dolphins' consistent failure in pass protection. Henne was sacked 11 times in three games and one quarter. And since taking over for Henne, the less-mobile Moore has already been sacked 11 times.
Pass protection could be an issue again for the Dolphins on Sunday when they play on the road against the New York Giants, who are tied for first in the NFL with 21 sacks.
"Their front four is pretty impressive," Moore said of the Giants' defensive front. "They cause a lot of problems with just those guys so we need to be sharp up front. And they obviously have the ability to add guys on, whether its linebackers or secondary players."
Rosenfels, a career journeyman, came to the Dolphins with plenty of experience but not much in recent years. He hadn't - and still hasn't - completed an NFL pass since 2008. And neither has Losman, who originally worked out with the Dolphins after Henne suffered his season-ending injury.
Losman's goal, then, is to learn the Dolphins' offense as quickly as possible. He has to, given that he's now only an injury away - a play away, really - from being the Dolphins' first-string quarterback.
"I just want to show the players - I don't know what they heard about me before or what - I just want to show them I work hard," Losman said. "I'm here to learn the offense. Like, right now - as fast as I can. And that's just - that's what I'm here for."
After his time with the Bills ended following the 2008 season, Losman spent part of the 2009 season with Oakland, where he played in one game and attempted one pass. He spent part of the 2010 season with Seattle and he didn't play in a game.
Losman was the 22nd overall selection in the 2004 draft and has started 33 of his 43 career games.
"The hardest part in the NFL, once you leave the team that you're from or whoever drafted you, is sticking somewhere," Losman said. "You know, you just go down the line of the list of coaches that I've played for ... I'm here to work and hopefully I just stick."
If he does indeed stick, Losman will reverse a trend and put a stop to the Dolphins' ongoing quarterback carousel.