The standard player contract (SPC) of a Group 3 unrestricted free agent can contain a specific clause which prevents the player from being involuntarily moved from their current team. There are two types of clauses, the no-trade clause and the no-movement clause.
As you might imagine, the no-trade clause prevents a player from being traded to another team without their express permission. A no-movement clause not only prevents the player from being traded, but also prevents their relocation by loan or waivers as well. So a player with a no-movement clause could not be sent down to the AHL without agreeing (which, as you might imagine, is probably unlikely).
A no-movement clause, however, does not prevent a team from being able to buy-out the player. From section 11.8(b):
(b) A no-move clause may prevent the involuntary relocation of a Player, whether by Trade, Loan or Waiver claim. A no-move clause, however, may not restrict the Club’s buy-out and termination rights as set forth in this Agreement. Prior to exercising its Ordinary Course Buy-Out rights pursuant to Paragraph 13 of the SPC hereof, the Club shall, in writing in accordance with the notice provisions in Exhibit 3 hereof, provide the Player with the option of electing to be placed on Waivers. The Player will have twenty-four (24) hours from the time he receives such notice to accept or reject that option at his sole discretion, and shall so inform the Club in writing, in accordance with the notice provisions in Exhibit 3 hereof, within such twenty-four (24) hour period. If the Player does not timely accept or reject that option, it will be deemed rejected.
One interesting thing to note, is that if a player were to be traded before their no-trade or no-movement clause became effective (which is the case with both Mike Richards and Jeff Carter), the acquiring team is not required to provide that same clause to the player moving forward. They have the option to keep it, or be rid of it. From section 11.8(a):
(a) The SPC of any Player who is a Group 3 Unrestricted Free Agent under Article 10.1(a) may contain a no-Trade or a no-move clause. SPCs containing a no-Trade or a no-move clause may be entered into prior to the time that the Player is a Group 3 Unrestricted Free Agent so long as the SPC containing the no-Trade or no-move clause extends through and does not become effective until the time that the Player qualifies for Group 3 Unrestricted Free Agency. If the Player is Traded or claimed on Waivers prior to the no-Trade or no-move clause taking effect, the clause does not bind the acquiring Club. An acquiring Club may agree to continue to be bound by the no-Trade or no-move clause, which agreement shall be evidenced in writing to the Player, Central Registry and the NHLPA, in accordance with Exhibit 3 hereof.
The Flyers currently have five players with no-trade clauses: Scott Hartnell, Ruslan Fedotenko, Braydon Coburn, Luke Schenn, and Nicklas Grossmann. They also have four players with no-movement clauses: Danny Briere, Kimmo Timonen, Chris Pronger, and Ilya Bryzgalov.