Volcano magma chamber
You might get a lava seepage, but I doubt it. The cross-sectional area of a borehole is small compared to the total cross sectional area of fractures that are there already. Note that volcanoes bulge quite markedly due to lava up-welling and deformation due to magma pressure, so the volcano is invariably well fractured. A small hole is likely to fill up with magma rapidly, which would cool and solidify against the country rock, thereby plugging the hole - unless the borehole was very close to a gassy magma chamber. However, there might be exceptions in that very small fraction of volcanoes that are of the 'Plinian' type, in which exceptionally high gas pressures can occur. But then, nobody in their right mind would drill into a potentially Plinian type of volcano!