I would like to run Damn Small Linux 4.4.10 on an old computer but a friend of mine said it could pose a possible security risk because it is no longer under development but dormant. Would anyone like to help me out on this question please.

Everything depends on the purpose of use :-)

I can't speak much to the security question (though I doubt you'd be opening yourself to a bevy of huge risks if you're just using this as a desktop for personal use, without much sensitive data), but, if you're looking for an extremely light system for older hardware, check out tinycore and/or slitaz. They're both in active development.

Most of the security holes that get found affect servers rather than home computers, particularly if you have a good router, but it can be very frustrating to use a dead distro with a declining user base to seek help from.

It depends on how small your system is. You can run AntiX and Vector Light, complete with GUI, in just 64MB. Anything less than that and you're probably down to command line only. SliTaz would need more memory. Tiny Core is more of a kit for putting your own system together, unlike a conventional distro where you can just install and go.

vote for www.tinycorelinux.com
see my blog in this webpage

What are the hardware specs of the computer?