I'm an insect sociologist, so let me explain. Firstly, people often underestimate the hardiness of an ant, many ants can bounce right back after an apparent crushing by the average human boot or shoe. They have built in defence mechanisms that allow them to instinctively play dead at the sign of danger. Leading theory is that this is latent behaviour from their genetic history as part of the canine family, meaning that early humans may have actually taught the ants how to later survive against attacks from future humans, how cool is that?!

I should note that the survivability of a crushing depends on many factors like the softness of the boot, weight of the person doing the stepping, and availability and response time of emergency care, which is often required in extreme cases.

Secondly, regarding the family structure of the ants and how they provide for their families in the eventuality of a fatal crushing of the breadwinning ants... they have a societal structure that promotes the inherent care for those left behind. Widow ants and orphans are often adopted into the family unit (cluster) of close friends and co-worker ants and treated as one of their own. The economic stability of ant society means that it is not uncommon for only one working worker ant to provide enough wealth and support for several dozen depend-ants.

If the leading breadwinner of an ant family cluster is killed while at work and the cluster is already at breaking point financially, it is time for the younger generations to step up and take his place. There is often a considerable insurance payout to aid the transition, but it is rarely the kind of sum a human would expect upon death (their bodymass being much lower, they are worth less upon death).

Of course, ants do not follow a patriarchal societal structure like many other insects, so the breadwinning worker ants are often female too, this means that any member of a cluster could potentially step up to take the place of a crushed worker. Ants are actually one of the more progressive species when it comes to gender equality, many believe this is because of the amount of free time the vast majority of the population is afforded, leading many to study the arts and philosophy among other pursuits of the mind.
I hope this answers your question a little, of course there are many other factors, but i'm on mobile so I couldn't go into too much depth.