Alternative would be to drain it into a holding tank and, what, send somebody in to fix it? Who?
You identify the operational error in salt chemistry that has lead to losing some of the storage vessel material, and then you perform engineering analysis on the new resultant factor of safety. If necessary, next fueling cycle you shut down the reactor and perform remediation actions.
Salt chemistry monitoring is a critical part of a MSR operation. The fissile material is slowly exhausted in the reaction and needs to be replaced, while the byproducts need to be removed. The nuclear reaction causes some transmutation of every element it irradiates, which means you get a predictable but diverse set of contaminants that need to also be removed.
The molten salt corrodes everything it comes in contact with, and the radiation also degrades the materials in wild ways. One study I read estimated that directly exposed tungsten would transmute into rhenium at the rate of 1% per year, and that the newly created rhenium would transmute into osmium at the same rate. Basically, it will take an army of people much much smarter than me to plan for all the issues that might come up during the operation of a MSR.
There are many startups backed by billions of dollars trying to find a good solution. One of my favorites simply designs in 8 containment vessels and a crane into the reactor chamber. They plan to just pick up the top of the reactor and move it into a new vessel every 7 years or so.