Of computing platforms, personal computers now have less than 50% of the market. https://gs.statcounter.com/platform-mar ... ile-tablet. My guess is that statistic reflects that lower cost of owning, and the greater ease of carrying, an android device where the primary intent is interpersonal communication.
Only about 3.01% of personal computers run Linux, https://gs.statcounter.com/os-market-sh ... worldwide/ and there are hundreds, if not thousands, of Linux operating systems a user can choose. Puppy Linux users make up a small share of them, https://distrowatch.com/, a niche within a niche. The 'Lion's Share' of personal computers is still Windows which system has a 30 year lead on software specialized for business.
Linux in general, but Puppy Linux in particular, is not a 'target rich' objective attracting the attention of 'Web-pirates'. Puppy Operating systems are downloaded as compressed packages from reasonably secure websites, as are pets, debs and other packages various Puppys may use. Adulteration of these would require some type of 'man-in-the-middle' attack.
That leaves only the post deployment use of a Puppy in accessing the web as a vector for contaminating a User's operating system. Most Linux operating systems function as 'a unified system' constantly writing to 'Storage' preserving changes. Puppys operating under PupMode12 do that. But Puppys don't have to operate under PupMode 12. Puppys can be run under PupMode 5 (without a Storage Medium to write to) or PupMode 13, where only user selected changes are preserved. Under PupModes 5 and 13, if the User does not preserve changes, whatever changes may exist in RAM are wiped. Long ago I advocated that when running PupMode13, any desired additional software requiring installation be downloaded, stored, but not installed until after a reboot; and then immediately installed and a Save executed before again accessing the Web.
As far as I know --and correct me if I'm wrong-- malware designed to search for and then transmit sensitive information, or modify an operating system are sufficiently complex that their size requires they be downloaded as components, then assembled by running one of those components. A properly hardened web-browser will deter the downloading of components. And the absence of any component which was wiped from memory on shutdown/reboot will prevent the accumulation of components needed to be assembled.
Without regard to how many flaws there are in its 'old' kernel, the threat malware poses to a Puppy exits in the realm of possibilities, not probabilities.