Having the option to ditch offspring when conditions are too harsh to sustain them is one of the survival advantages of being a marsupial, rather than a placental, mammal. A starving mother kangaroo can leave a joey behind, save herself, and live to breed again when conditions improve.
Even today, some parents may willingly give up custody of their children if they cannot afford to raise them. Many countries have "safe haven laws" where a parent can leave a child (up to a certain age) at a hospital, clinic, police station, or firehouse and not be charged with child endangerment.
In Nebraska the original safe haven law allowed any child under 18 to be left at a hospital. Resulting in 35 non-infant children being left at hospitals.
In some cases the only way a parent can get a dangerously mentally disturbed child the help they need is to surrender their parental rights to the state.
Numerous studies with monkeys has put forth the theory that not only is there a problem with outright neglect, but even emotional coldness or social isolation can create socially disordered (or autistic) children later on. The same studies found that a surrogate would produce strange but okay children. So, basically, it's better to be Raised by Wolves than have Parental Abandonment.
Some animals, such as elephants and orca whales, learn how to raise young by watching family members do it. If a captive individual doesn't get this opportunity, it greatly increases the chance of the animal not caring for her offspring.