32bit software

No.

Also see the following from 32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

Apple's transition to 64-bit technology is now complete. Starting with macOS Catalina, 32-bit apps are no longer compatible with macOS. If you have a 32-bit app, please check with the app developer for a 64-bit version.

This free app, GO64, will show you which of your current apps will not work in Catalina when you upgrade to that OS and will have to be upgraded or replaced.

One alternative is to get an external SSD and clone your current boot drive to it with Carbon Copy Cloner  or SuperDuper and boot from it when you need to use one of the older 32 bit apps.

genozeno Said:

"32bit software: Will Catalina be able to use 32 bit software"

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Apple Software? No - Catalina is 64bit-Only.

but...

Run on a Windows Virtual Machine:

Install this on a Virtual Machine of Microsoft Windows, and it would work on that - should it be installed on the Virtual Machine.

More on Virtual Machines:

Consider using a Virtual Machine(VM) (Windows-in-a-window). You would open Windows-Only Compatible items on it, including hardware like printers and scanners that are not macOS compatible. All would be accessed and would operate as desired on the VM. Virtual Machine applications include VMWare Fusion and Parallels. Learn more here: What Is a Virtual Machine? - VMWare Support.

Not even a little bit. Only 64-bit.