Owner Suleyman Kerimov withdrew the majority of his funding from Anzhi last year, leading to a mass exodus of players that saw them slide down the Russian Premier League table.
The days of Samuel Eto'o, Willian and Roberto Carlos playing for the club are long gone, with a dreadful start to their domestic season - which saw them draw eight and lose 11 of their first 19 league games - leaving them stranded in the relegation zone.
Despite their plight at home, Anzhi have surprisingly prospered in the Europa League, qualifying from a group that included Tottenham, Tromso and Sheriff.
The Russians were one of just two sides to make it through the group stages with a negative goal difference after scoring just four goals in Group K.
A 2-0 win at Genk last month in the second leg of their last 32 clash saw them move a step closer to the quarter-finals.
With the Russian Premier League taking a mid-season break of three months, a series of friendlies gave Anzhi the chance to regain form, and that they did, winning all four.
And their success against Genk was followed by a 1-0 league win over Rubin Kazan on Sunday, secured thanks to Alexander Bukharov's late goal.
Anzhi, for whom Alexander Troshechkin remains sidelined, are still rooted to the foot of the league table but are in good spirits ahead of the match in Alkmaar on Thursday.
And they do have good memories of playing AZ after beating them 6-0 in the 2012-13 UEFA Europa League play-offs. The Russian side won the second leg 5-0 in the Netherlands, although only two players who featured remain at the club.
AZ are enjoying far more success than their opponents domestically, sitting seventh in the Eredivisie after successive 4-0 wins over RKC Waalwijk and Heracles.
Aron Johannsson and Steven Berghuis have starred recently for AZ, who were unbeaten in the Europa League's group stages.
Johannsson scored twice on Saturday and has netted 16 goals in 26 Eredivisie appearances this season.
"It was quite enjoyable to watch," AZ coach Dick Advocaat - who formerly managed Russia - told De Telegraaf after the win.
"Just like against RKC Waalwijk, when we won 4-0. There was a lot of movement. If we lose, Heracles came within four points of us. Now we have put (10 points between us)."
AZ won three and drew three in Group L to finish in first place with 12 points and then edged Slovan Liberec in the last 32, winning 2-1 on aggregate.
Johann Gudmundsson has scored five goals in 10 Europa League appearances this season for AZ, but Celso Ortiz, Dirk Marcellis and Jan Wuytens could all miss out due to injury.
