DB Multiverse

Yes, you've heard it, Kakarotto and Raditz survival (and Vegeta and Nappa) are all planed by the tyrant, and not a lucky coincidence.
Note that in DB, it's officially told that it was the case for Vegeta.
For the two brothers, it's DBM canon, and totally invented by us.

Of course, Freeza will have totally forgotten about the 4th Saiyan 20 years later. Raditz didn't become elite, so they didn't care much about them.

You now know the mother's name of the two brothers. It's also invented by us. Both their parents are "elite" (mean more than 10,000 in power), that's why everyone is so disappointed in their sons (or a reason to laugh at, for the other children).
By the way, in Saiyan society, you're not born elite, you are it due to your power. That's why Baddack was born low class, and is now elite.