I'm not entirely sure about exact pay day being the first "morning after return from the front line". Troops usually rotated through several lines of trenches before they had a rest period, and there are plenty of accounts of variations in pay timings in the personal accounts of individual soldiers. Not to mention that paybook fraud was rife within the British and Dominion armies. But I'll answer this question first by saying that outstanding pay was probably sent to his next of kin, and secondly giving a quick run down on widows pensions.

I spent quite a while digging but I'm yet to find anything that clarifies it one way or the other, but it's most likely that outstanding pay would have simply been forwarded to the soldiers next of kin or any declared dependents. Usually soldiers who were married, to-be married or in defacto relationships would list their partner as their next of kin. More than that they also had the opportunity to list their partners or any family members who were dependent on them. Once declared the soldier could then have part, or all, of his pay sent directly to his dependents, with an account usually run through the local post office. As an addition to their daily pay, Australian soldiers (I'm not sure about British) also earned deferred pay. This money was held in trust and only paid out to soldiers on their discharge, or to their next of kin on their death. Given the deferred pay and the option for dependent pay, it's pretty safe to assume any outstanding pay would have simply been added to the amount paid out on a soldier's death.

Beyond the soldier's pay, British war widows were also eligible for an Additional Allowance of £5 on a soldiers death, with £1 extra for each dependent child. I've uploaded a pamphlet from 1918 which describes the war pensions for Britain.

Widows pensions themselves were set at a variety of different rates depending on the rank of the deceased and the number of dependents left behind. The main measure used was the rate of a man deemed fully disabled after the war at their last service rank.

Using Australian numbers from the War Pensions Act 1914 here:

If a private, whose daily wage was 6s, was fully disabled by war wounds, he was entitled to £52 a year, distributed weekly. His widow would receive that £52 a year (a pound a week), with up to an extra £13 per child per year, roughly 5s per week.

According to the British pamphlet:

The widow of a private would receive 13/9 per week (about £36 per year) with an extra 6/8 for the first child under 16 and 5s for the next with 4/2 for any further children.