Make T[never] = never instead of erroring or being any

src/compiler/checker.ts

@@ -8151,6 +8151,9 @@ namespace ts {
                     }
                     return indexInfo.type;
                 }
+                if (indexType.flags & TypeFlags.Never) {
+                    return neverType;
+                }
                 if (accessExpression && !isConstEnumObjectType(objectType)) {
                     if (noImplicitAny && !compilerOptions.suppressImplicitAnyIndexErrors) {
                         if (getIndexTypeOfType(objectType, IndexKind.Number)) {

tests/baselines/reference/indexingTypesWithNever.js

@@ -0,0 +1,121 @@
+//// [indexingTypesWithNever.ts]
+type TestObj = {
+  a: string;
+  b: number;
+};
+
+// Should be never but without an error
+type Result1 = TestObj[never];
+
+type EmptyObj = {};
+
+// Should be never but without an error
+type Result2 = EmptyObj[keyof EmptyObj];
+
+declare function genericFn1<T>(obj: T): T[never];
+
+// Should be never
+const result3 = genericFn1({ c: "ctest", d: "dtest" });
+
+declare function genericFn2<T extends { [ind: string]: string }>(
+  obj: T
+): T[never];
+
+// Should be never
+const result4 = genericFn2({ e: "etest", f: "ftest" });
+
+declare function genericFn3<
+  T extends { [K in keyof T]: T[K] },
+  U extends keyof T,
+  V extends keyof T
+>(obj: T, u: U, v: V): T[U & V];
+
+// Should be never
+const result5 = genericFn3({ g: "gtest", h: "htest" }, "g", "h"); // 'g' & 'h' will reduce to never
+
+
+declare const obj: {a: string, b: number}
+declare const key: never
+
+const result6 = obj[key]
+
+// Expanded examples from https://github.com/Microsoft/TypeScript/issues/21988
+type RequiredPropNames<T> = {
+  [P in keyof T]-?: undefined extends T[P] ? never : P
+}[keyof T];
+
+type OptionalPropNames<T> = {
+  [P in keyof T]-?: undefined extends T[P] ? P : never
+}[keyof T];
+
+type RequiredProps<T> = { [P in RequiredPropNames<T>]: T[P] };
+type OptionalProps<T> = { [P in OptionalPropNames<T>]?: T[P] };
+
+type Match<Exp, Act> = [Exp] extends [Act]
+  ? ([Act] extends [Exp] ? "Match" : "Did not match 2")
+  : "Did not match 1";
+
+type ExpectType<Exp, Act> = Match<Exp, Act> extends "Match"
+  ? ({} extends Exp ? Match<Required<Exp>, Required<Act>> : "Match")
+  : "Did not match";
+
+type P3 = { a: string; b: number; c?: boolean };
+type P2 = { a: string; c?: boolean };
+type P1 = { c?: boolean };
+type P0 = {};
+
+type P3Names = RequiredPropNames<P3>; // expect 'a' | 'b'
+type P2Names = RequiredPropNames<P2>; // expect 'a'
+type P1Names = RequiredPropNames<P1>; // expect never
+type P0Names = RequiredPropNames<P0>; // expect never
+
+declare const p3NameTest: ExpectType<"a" | "b", P3Names>;
+declare const p2NameTest: ExpectType<"a", P2Names>;
+declare const p1NameTest: ExpectType<never, P1Names>;
+declare const p0NameTest: ExpectType<never, P0Names>;
+
+type P3Props = RequiredProps<P3>; // expect { a: string; b: number }
+type P2Props = RequiredProps<P2>; // expect { a: string; }
+type P1Props = RequiredProps<P1>; // expect {}
+type P0Props = RequiredProps<P0>; // expect {}
+
+declare const p3Test: ExpectType<{ a: string; b: number }, P3Props>;
+declare const p2Test: ExpectType<{ a: string }, P2Props>;
+declare const p1Test: ExpectType<{}, P1Props>;
+declare const p0Test: ExpectType<{}, P0Props>;
+
+type O3 = { a?: string; b?: number; c: boolean };
+type O2 = { a?: string; c: boolean };
+type O1 = { c: boolean };
+type O0 = {};
+
+type O3Names = OptionalPropNames<O3>; // expect 'a' | 'b'
+type O2Names = OptionalPropNames<O2>; // expect 'a'
+type O1Names = OptionalPropNames<O1>; // expect never
+type O0Names = OptionalPropNames<O0>; // expect never
+
+declare const o3NameTest: ExpectType<"a" | "b", O3Names>;
+declare const o2NameTest: ExpectType<"a", O2Names>;
+declare const o1NameTest: ExpectType<never, O1Names>;
+declare const o0NameTest: ExpectType<never, O0Names>;
+
+type O3Props = OptionalProps<O3>; // expect { a?: string | undefined; b?: number | undefined }
+type O2Props = OptionalProps<O2>; // expect { a?: string | undefined; }
+type O1Props = OptionalProps<O1>; // expect {}
+type O0Props = OptionalProps<O0>; // expect {}
+
+declare const o3Test: ExpectType<{ a?: string; b?: number }, O3Props>;
+declare const o2Test: ExpectType<{ a?: string }, O2Props>;
+declare const o1Test: ExpectType<{}, O1Props>;
+declare const o0Test: ExpectType<{}, O0Props>;
+
+
+//// [indexingTypesWithNever.js]
+"use strict";
+// Should be never
+var result3 = genericFn1({ c: "ctest", d: "dtest" });
+// Should be never
+var result4 = genericFn2({ e: "etest", f: "ftest" });
+// Should be never
+var result5 = genericFn3({ g: "gtest", h: "htest" }, "g", "h"); // 'g' & 'h' will reduce to never
+var result6 = obj[key];