[Solved] Give all players in server a badge when remove event fired?

Yep, all you need to do is use badge service

In the code they provide, they do

local BadgeService = game:GetService("BadgeService")

local function awardBadge(player, badgeId)
    -- Fetch badge information
    local success, badgeInfo = pcall(function()
        return BadgeService:GetBadgeInfoAsync(badgeId)
    end)
    if success then
        -- Confirm that badge can be awarded
        if badgeInfo.IsEnabled then
            -- Award badge
            local awarded, errorMessage = pcall(function()
                BadgeService:AwardBadge(player.UserId, badgeId)
            end)
            if not awarded then
                warn("Error while awarding badge:", errorMessage)
            end
        end
    else
        warn("Error while fetching badge info!")
    end
end

You are able to do this on the server, no need to fire the client with remote event/functions.

To ensure everyone in the server receives the badge, just use player service and use the function GetPlayers() in a loop.

This should be all you need, good luck! If you need further help, please make sure to edit your post with the code you use.

If you have any questions, let me know and I'll respond when I can. Make sure to mark this solution as correct if it works.