AllowEmptyCollection, as the name suggests, allows an empty array to be assigned to a mandatory parameter:

function Test-AllowEmptyCollection {
    [CmdletBinding()]
    param (
        [Parameter(Mandatory)]
        [AllowEmptyCollection()]
        [Object[]]$Parameter1
    )
}

This will allow the command to be called with an explicitly empty array:

Test-AllowEmptyCollection -Parameter1 @()