so i searched about this subject who i interested with it several times
and not get any clearly answer
but the targed distro is the distros who ran from ram (antix, mx linux, puppyos..)
so in the last as a debian user can i install them with this method without taking full partition (like dual booting mxlinux with debian, just edit the grub file like they said)
Frugal installations are similar or even perhaps the same I guess to minimal installations.
It's not quite clear to me what you are after, so I'll make a few general observations which may be of interest bouncing off your text.
Distros that run from RAM can often be installed, but when installed, these installations will always take up partition space on a drive, that is like a hard disk or SSD. The live disks issued by various distros like debian, fedora, antix, mint, mx etc. can be booted up into RAM, and then installed at the discretion of the user. When installed, it's to partitions on a drive, so they take up disk space.
For grub to boot a distro that is not on the drive, it can be configured to boot a live disk that has been plugged into a usb socket. In that way, the live distro could be called by grub, instead of using the perhaps more common method to boot the usb through bringing up the boot menu of the machine and selecting the live disk from that menu. One disadvantage of configuring grub in this way is simply the unnecessary configuration effort in the face of the availability of boot menus on modern machines. On older machines, one could configure the boot order in the BIOS to select a usb to boot first, so either new or old machines, it's unnecessary to bother with configuring grub for this purpose.
If all one want's is a frugal or minimal installation of debian, a well-tried and proven method is to install debian from the netinstall image, but de-select all the desktops and superfluous packages. This will leave a system that boots to a text prompt, after which the user can install just what they want and keep the system as small as they like, within the limits of what debian provides. The last time I did this with current debian stable the disk size taken up was about 800MB. One gets a bootable installation with networking and basic system tools.
There is a thread on the size of distros which may be of interest here:
https://www.linux.org/threads/for-the-fun-of-it-how-big-is-your-distro-installation.57996.