How to do when a player dies to be removed from a table?

I would create a function that finds the player by name, and removes it based off of the current index. When you remove an object from a table like you did in line 19, it moves the other elements down, making the i index incorrect.

function removePlayerByName(plyrnm)
    local i = 1
    while playersAlive[i].Name ~= plyrnm and i <= #playersAlive do
        i += 1
    end

    if playersAlive[i] then
        table.remove(playersAlive, i)
    end
end

And:

for i = 1, #playersAlive do
    local plyr = playersAlive[i]
    plyr.Character:WaitForChild("Humanoid").Died:Connect(function()
        removePlayerByName(plyr.Name)
    end)
end

I think it would be better to do this though:

function checkGameCondition(plyr)
    if workspace.GameMode.Value == "FFA" then
        removePlayerByName(plyr.Name)
    end
end

game.Players.PlayerAdded:Connect(function(plyr)
    plyr.CharacterAdded:Connect(function(char)
        char:WaitForChild("Humanoid").Died:Connect(function()
            checkGameCondition(plyr)
        end)
    end)
end)

I think something like this would work, this would remove the character from the table and replace it with nil(basically doesn't exist).

for i, v in pairs(playersAlive) do
    v.Character.Humanoid.Died:Connect(function()
        playersAlive[i] = nil
    end)
end

I think the main issue was with the while loop, specifically the use of return instead of continue. I made a lot of changes here and there and did my best to explain each one.

local sword = game.ReplicatedStorage.ClassicSword

if workspace.GameMode.Value == "FFA" then
    --Use GetChildren() to return an array of the spawns

    local spawnsTable = chosenClone.Spawns:GetChildren())

    local playersAlive = {}

    for _, player in ipairs(game:GetService("Players"):GetPlayers()) do
        local character = player.Character

        if not character then
            continue
        end

        table.insert(playersAlive, player) --table.insert shifts the table

        --connect the died event here, dont make a new loop
        --edit: table.find returns an index, useful for removing them

        character.Humanoid.Died:Connect(function()
            table.remove(playersAlive, table.find(playersAlive, player))
        end)

        player.Character:SetPrimaryPartCFrame(spawnsTable[math.random(1, #spawnsTable)].CFrame)

        sword:Clone().Parent = player.Backpack
    end

    --main issue here, the use of return was unneeded and dont use wait()

    while true do
        wait(1)

        if #playersAlive < 2 then
            break
        end
    end

    --check if playersAlive[1] exists in the case of a tie

    local winner = playersAlive[1]

    if winner then
        editGUI("ChangeText", winner.Name .. " wins!")

        wait(3)

        winner:LoadCharacter()
    else
        editGUI("ChangeText", "There was a tie!")
    end

    chosenClone:Destroy()
end