If

The past tense of dig is dug, surely jig and jug follow the same rule. The basis of the English language is far more complex.

The verse below is extreme frippery. Reflections of musings of three letter words ending in ‘ig’ that have a corresponding ‘ug’ ending word.

Big bug in the fug
did not dig the fig
He dug the Mig on
A rig.

Pig the pug plays tig
On a rug and does
Jig in a jug on
A tug

The first draft was constrained by four single syllable words per line, the first letter of the three letter words, alphabetically, dictated the order of the lines, and ug after ig.

A big bug did
Dig and dug not
A fig in the fug
Nor jig in a jug

Mig on a mug
Pig the pug goes
To rig a rug
For tig and tug