Visiting beavers from upstream
Your settlement should get visitors from upstream beaver colonies. (A random event.) They float down the river on their backs, and join your settlement for a period. They sleep in tents (temporary instant buildings places in random clear area near your main settlement.) They eat your food and drink, work if needed, and then they leave a few days later by getting back in the river and floating off again. Every beaver in your settlement should get a small fun and education boost for the duration. Working hours reduced by one.
As a related random event, a small group of your unemployed beavers (given a large population and excess resources) should also just decide to uproot. They take some food and wood, then jump into the river and float off for new adventures downstream. (This is, of course, what has happen elsewhere upstream to lead to the immigration event.)