@MistressoftheDarkSide post on the last page explains it well. Better than I can but I'll try. Although I suggest you read her post which answers your question on how investing in good public services pays off and reduces the amount of dependancy. Other PP have also given good explanations but I can't remember who right now and don't have the time to re-read the whole thread).
Here's an example. Someone I know. Used to work but developed health issues. Thanks to long NHS wait lists and delays, by the time she was diagnosed things had got much worse. If she'd been able to access good and early help she'd still be able to work.
Another example. Woman flees DV. There's a shortage of refuge spaces due to funding cuts but even if she finds a place often she'll then be 'moved on' to temporary accommodation. Which is often as Mistress says sub standard to say the least. It's definitely not somewhere for vulnerable DV victims (or their DC) to recover from trauma.
Also even if they get decent housing quickly people don't just recover overnight from very traumatic events. Not without time and or effective support. Support which is often lacking due to funding cuts.
The CMS system is a mess too, and that isn't only relevant to DV. So primary carer parents are left dependant on the state instead of the other parent paying for their kids. From @mathanxiety posts it sounds like we could learn something from the US when it comes to better enforcing child support.
Some DV victims will be physically damaged as well as emotionally. Can't remember if it's this thread or another one but a poster was left disabled and unable to work after a very violent assault by her ex.
If public services were better funded (and preferably not privatised) the women and children affected by DV in situations I described above would get timely and effective support, and many would be able to get off benefits.
(Regarding DV, I do wonder how many of the 'cut them all off benefits cuz personal responsibility' PP jump on posters in abusive relationships insisting the person immediately LTB and dismiss the poster's financial or other practical concerns with 'I'd rather live in a bin on benefits if it were me' posts?)