I think this is the broadcom-sta kernel driver: https://download.liveslak.org/bonus/...ent-x86_64.sxz

If so, you can certainly install it on the liveslack usb. The usb has a 'persistence' directory and all your disk writes go there and stay over reboots.

While it's not exactly the answer the OP is hoping for, the way I ended up resolving my Broadcom WiFi adapter woes was simply to replace the adapters with Atheros devices, so I no longer have to mess about with b43 firmware cutter and iffy proprietary drivers for the sake of an adapter that even then would only work with some routers. If Broadcom's attitude to the open source world is so poor then their hardware doesn't have a place in my machines. The Atheros devices were secondhand on ebay and cost next to nothing, I think one was about £1.50 including postage. It might be worth considering for the sake of an easier life.

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Amen to that!

OP wrote: Is why I suggested that ISO as it has the broadcom firmware for many cards on the full version not OT.

Heck yeah, if can eliminate the problem go for it, I have several that have "whitelist"
in the bios, can't change the cards or won't boot.

I can vouch for AntiX or MX at least; and there are others, but the Bluetooth almost never works. The WiFi is often enabled on live distros and I know how to install the BT driver once the software is installed to a hard drive, but getting it installed to a live distro USB has defeated me so far.

I have the same problem plus one other - if I try a live distro, I can be fairly sure of connecting at about 30/10M down/up and all seems fine. Install the distro to HDD though, and I find that the connection speed drops through the floor. Also, the BT often hangs, as though the system is doing something else in the background. If so, I have yet to find what it is. It’s intensely annoying. It always comes back, but in the meantime, the anger builds. Being that the chip is dual BT/WiFi, I wonder if there is a process that is affecting either the bus or the driver. I wish I knew. I’m on the verge of giving up on this netbook because of it.

This is on a HP Stream 14 with 2G ram and 32G HDD unexpandable. It’s galling. There must be a solution. It affects almost all distros I have tried so far. Any distros that can’t get the WiFi going live, get binned, as they often can’t find the USB Ethernet adaptor (there is no Ethernet port) either, so only when I have installed to HDD will I find if the problem is fixable.

So far, no viable solution with a lightweight distro that suits.

I've used Isomaster on Slackware to substitute kernels in numerous isos. It really shouldn't be very hard especially if you use the same basic naming conventions. For example, I rebuilt an iso for 12.2 with a 5.12 kernel substitution and the system installed and ran fine, supporting newer hardware not in existence back in 12.2 days. The reverse should work just as well. Obviously if you don't already have Isomaster installed and can't download anything that would be a lot harder. However, since Liveslak can be set for Persistence, I imagine simply copying in a desired kernel substitution on a running system should work similarly, even if you had to boot it first and add the new kernel to the boot options menu.