diff --git a/base/compiler/tfuncs.jl b/base/compiler/tfuncs.jl
index f8db243ce4dae..ac8aa0c639dc5 100644
--- a/base/compiler/tfuncs.jl
+++ b/base/compiler/tfuncs.jl
@@ -822,6 +822,7 @@ function getfield_tfunc(@nospecialize(s00), @nospecialize(name))
     if isType(s) || !isa(s, DataType) || s.abstract
         return Any
     end
+    s = s::DataType
     if s <: Tuple && name ⊑ Symbol
         return Bottom
     end
@@ -831,6 +832,9 @@ function getfield_tfunc(@nospecialize(s00), @nospecialize(name))
         end
         return Any
     end
+    # If no value has this type, then this statement should be unreachable.
+    # Bail quickly now.
+    s.has_concrete_subtype || return Union{}
     if s.name === _NAMEDTUPLE_NAME && !isconcretetype(s)
         if isa(name, Const) && isa(name.val, Symbol)
             if isa(s.parameters[1], Tuple)
diff --git a/src/jltypes.c b/src/jltypes.c
index 31a06e2bdc092..b7a58a3610027 100644
--- a/src/jltypes.c
+++ b/src/jltypes.c
@@ -1558,6 +1558,9 @@ static jl_svec_t *inst_ftypes(jl_svec_t *p, jl_typeenv_t *env, jl_typestack_t *s
         jl_value_t *pi = jl_svecref(p, i);
         JL_TRY {
             pi = inst_type_w_(pi, env, stack, 1);
+            if (!jl_is_type(pi) && !jl_is_typevar(pi)) {
+                pi = jl_bottom_type;
+            }
         }
         JL_CATCH {
             pi = jl_bottom_type;
diff --git a/test/compiler/inference.jl b/test/compiler/inference.jl
index 24ddd9a13dc1b..2758e510c9380 100644
--- a/test/compiler/inference.jl
+++ b/test/compiler/inference.jl
@@ -2910,3 +2910,10 @@ end
 
 # issue #37638
 @test !(Core.Compiler.return_type(() -> (nothing, Any[]...)[2], Tuple{}) <: Vararg)
+
+# Issue #37943
+f37943(x::Any, i::Int) = getfield((x::Pair{false, Int}), i)
+g37943(i::Int) = fieldtype(Pair{false, T} where T, i)
+@test only(Base.return_types(f37943, Tuple{Any, Int})) === Union{}
+@test only(Base.return_types(g37943, Tuple{Int})) === Union{Type{Union{}}, Type{Any}}
+