I will go a step further than Brent and say the entire discontinuity has to be excavated if you have any hope of rewelding the affected area with no porosity.
All dye penetrants are petroleum based, i.e., oil based, material with concentrated dye stuffs (yes, that is the technical term). As such, any remaining petroleum product will produce porosity. The amount of porosity is largely dependent on the volume of penetrant remaining in the unexcavated discontinuity.
Whether the porosity present is accepted or not is dependent on the welding standard that governs fabrication.
Some materials, i.e., aluminum alloys, will produce more than others, but there will be porosity present, either or both surface breaking or subsurface.
Best regards - Al