I've only been following the league for a few years so I'm wondering what kind of precedence there is for sacking a manager early during the season?
I think Shurmur will be 0-7 (@Ravens, @Giants, Bengals, @Colts) when Haslam takes over. We already know Joe Banner is likely coming in as an executive (probably to replace Holmgren?) and is quoted as saying he wants to work somewhere that requires a complete turnaround... well that's the Browns.
I think Haslam will blow it up. Get rid of Shurmur and Holmgren, possibly Heckert but I wouldn't mind if he stayed - he has hit more than he has missed in the draft (McCoy and Weeden were Holmgren overruling him)
But would an owner, a new owner at that, do this during the middle of the season?
I'm gonna go ahead and assume by 'manager' you mean 'coach', what with you being a Brit. To me it really depends on the owner. You don't really have the same pressure as in euro footie leagues where you might end up in a lower division, lose lots of money. In fact, sucking can get you a decent pick sometimes, that is if you can draft for shit.
There aren't that many in-season changes like there used to be, or maybe it's just my perception, but there is always remaining contract length of a coach and gm, paired with current-season success. I find that coaches in their penultimate year are often a target. First-year coaches are usually given at least another chance, unless they are absolutely inept, or work for the Raiders. New GM likely will go with his own candidate, for obvious reasons. Most coaches don't play on the last year of their contract as this is regarded as a good excuse for players to slack off to get rid off a coach. That's an interesting aspect about the NFL, compared to euro football.
For your team, if Holmgren goes, so does the coach. Even if he was decent, I'd expect a complete overhaul.
Btw, I think they should have a draft lottery similar to the NBA so that teams don't suck for the first overall.