diff --git a/base/compiler/typeutils.jl b/base/compiler/typeutils.jl
index ebb06a33a2d74..d6eb7305b1c8d 100644
--- a/base/compiler/typeutils.jl
+++ b/base/compiler/typeutils.jl
@@ -70,6 +70,15 @@ function typesubtract(@nospecialize(a), @nospecialize(b))
     if isa(a, Union)
         return Union{typesubtract(a.a, b),
                      typesubtract(a.b, b)}
+    elseif a isa DataType
+        if b isa DataType
+            if a.name === b.name === Tuple.name && length(a.types) == length(b.types)
+                ta = switchtupleunion(a)
+                if length(ta) > 1
+                    return typesubtract(Union{ta...}, b)
+                end
+            end
+        end
     end
     return a # TODO: improve this bound?
 end
diff --git a/test/compiler/inference.jl b/test/compiler/inference.jl
index 26371e7927005..fd2e6138e561d 100644
--- a/test/compiler/inference.jl
+++ b/test/compiler/inference.jl
@@ -2545,3 +2545,44 @@ end
 @test only(Base.code_typed(pickvarnames, (Vector{Any},), optimize=false))[2] == Tuple{Vararg{Union{Symbol, Tuple{Vararg{Union{Symbol, Tuple}}}}}}
 
 @test map(>:, [Int], [Int]) == [true]
+
+# issue 35566
+module Issue35566
+function step(acc, x)
+    xs, = acc
+    y = x > 0.0 ? x : missing
+    if y isa eltype(xs)
+        ys = push!(xs, y)
+    else
+        ys = vcat(xs, [y])
+    end
+    return (ys,)
+end
+
+function probe(y)
+    if y isa Tuple{Vector{Missing}}
+        return Val(:missing)
+    else
+        return Val(:expected)
+    end
+end
+
+function _foldl_iter(rf, val::T, iter, state) where {T}
+    while true
+        ret = iterate(iter, state)
+        ret === nothing && break
+        x, state = ret
+        y = rf(val, x)
+        if y isa T
+            val = y
+        else
+            return probe(y)
+        end
+    end
+    return Val(:expected)
+end
+
+f() = _foldl_iter(step, (Missing[],), [0.0], 1)
+end
+@test Core.Compiler.typesubtract(Tuple{Union{Int,Char}}, Tuple{Char}) == Tuple{Int}
+@test Base.return_types(Issue35566.f) == [Val{:expected}]