What happens if my opponent plays a site nearby Cursed Land that would silence it (e.g. Fields of Phyxis, Smokestacks of Gnaak)?
They will not
lose life. This is because
Cursed Land's
ability is a
triggered ability, but
Fields of Phyxis and
Smokestacks of Gnaak both have passive abilities which apply ongoing effects, and ongoing effects are applied before triggers.
