What did a medieval beggar earn?
Alms only, and giving to anyone fit to work was a crime.
Scraps and a wooden bowl. A single gram of gold would be a very good month.

Where the money came from
The Black Death killed an estimated 30 to 40 per cent of England's people, and the workers who survived were suddenly in great demand. On 18 June 1349 Edward III ordered every able-bodied man and woman under sixty, free or unfree, with no land or trade of their own, to work for whoever asked, at the wages paid before the plague. Anyone who refused could be sent to gaol. A beggar had no wage at all, only alms, and the same law struck at the alms. Beggars fit to work were blamed for idleness, vice and even theft, and anyone who gave them anything out of pity risked prison. The ban covered only those able to labour. For the rest, help came mostly from the Church. Monasteries were the main source of relief for the poor, and hospitals gave the sick, the poor and travellers food, shelter and prayer. Their halls had beds along the walls and a chapel joined on, with little privacy, and some almshouses would not take beggars at all. In 1388 the Statute of Cambridge went further. A labourer found wandering without a letter from the justices went into the stocks, and each district had to keep its own poor who were too old or sick to work. So a beggar fit to work had two choices: a labourer's old wage, or gaol.
Sources: en.wikipedia.org · en.wikipedia.org 2 · en.wikipedia.org 3 · en.wikipedia.org 4
What a beggar's pay bought in 1350
a farthing loaf of bread: out of reach, with no pay at all
a dozen eggs: out of reach, with no pay at all
Every price of 1350, with its source, is on the prices page.