Answered this on the Wolf Q&A channel in the official WolfQuest Discord; there are some other answers of mine in older threads here, but this is the most cohesive answer to your question.
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Abandonment [of pups] is possible but depends on the context. In a scenario where abandonment is on the table, survival of the pups depend on the age of the pups and which mate dies; the likelihood of survival probably influences abandonment. If the pups at an age where they still require milk for example and the mother perishes, then their abandonment and/or death is likely if there is not another lactating female present.
Abandonment is also more probable if the parent present with the pups is in life-threatening danger, according to a wolf keeper named Jackie at the Minnesota Zoo:
“Something to remember is that while a mother wolf has bonded with her pups, it is unlikely that she would die protecting them. She would abandon them after putting up a fight if her life was definitely in danger. This may sound cruel but many pups wouldn't survive without their mother so what would be the purpose of her dying. Pup survival is not easy. We don't know what the wolves are thinking, but there is always the next breeding season.”
viewtopic.php?f=6&t=465#p10583
Otherwise, especially if the pups have been weaned, wolves are capable of caring for the pups by themselves if the other wolf dies. Thus, the pups need not be abandoned. Still, this is not without its challenges.
“For wolves, monogamy does not appear to be obligate in the sense defined by Kleiman (1977), meaning that care by the father (fig. 2.6) is not essential under all conditions. At least one female wolf raised pups, apparently from birth, without help from other pack members (Boyd and Jimenez 1994). Other examples include situations in w
hich mothers, and in one case a father, raised pups after losing a mate (Boyd and Jimenez 1994; D. W. Smith, unpublished data).”
L. David Mech, Wolves: Behavior, Ecology and Conservation, page 50
Original question on Discord as it relates to mates: "Although wolves are monogamous, there are some cases where a male wolf(usually a rogue) mates with more than one female, or a subordinate female denning alone in her pack, but never bonding with the wolf she mated. Why would that happen?"
I didn’t find a definitive answer that addresses why but I’ll do my best to answer this question.
If the extra, non-dominant female in a pack is pregnant, Mech actually notes that the first culprit to be suspected would be the dominant male “even if the extra female were his daughter” due to inbreeding being a documented occurrence. However, in wild wolf packs, this is relatively rare (see my answer about inbreeding probabilities in this channel). The more likely answer would be a wolf from another pack or “outsiders through temporary liaisons” (*Wolves: Behavior, Ecology and Conservation, page 3*). Some of these wolves may fall into the category of pack “adoptee;” most pack adoptees are male, are one to three years of age, and are adopted anywhere from February to May. **Most adoptees stay with their new packs for a few days** but sometimes stay up to a year. Outside of regular adoptees, a male wolf that has been taken in to replace the breeding female’s mate may breed with her mature daughters, if present.
If present in a pack, non-dominant, mature female wolves need sufficient nutrition and low stress to be able to breed; sometimes this does not always occur due to a lack of food availability or pressure from the dominant animals (page 4).
So, if there is a successful mating, what’s the probability of abandonment?
The answer I found that addressed abandonment in general terms is that because the breeding period for wolves is so limited, there is “less incentive” for wolves to abandon pregnant mates in search of other females to pair/breed with.“Theoretically there is little ultimate cost to males that stay with their mates and help care for pups … females are unlikely to succeed in raising young alone”
(page 45).
My guess for the reasons behind abandonment/lack of bonding in a pair if it were to occur would be harassment from the dominant wolves, the presence of food stress or being in an area “where all suitable areas [for territory] are already defended (i.e., ‘saturated populations’)”
(page 38).