The Gregorian Mass is offered exclusively for the soul of the deceased person for thirty consecutive days, period during which the celebrant priest cannot apply any other intentions with a stipend.
That is why an offering is usually requested: to help support the priest in his pastoral task and his daily life during those days (the offering is equivalent to what would be given for thirty individual Masses, one per day) and it is what a priest, minimally, would use during the month to live: 300 dollars (or its equivalent in another currency), which is what the Holy See sets.
In the case of not being able to offer that money, something similar can be offered so that the priest can subsist during the month.