Don't cache non-existent Zig cache directory

post.js

@@ -1,3 +1,4 @@
+const fs = require('fs').promises;
 const core = require('@actions/core');
 const github = require('@actions/github');
 const cache = require('@actions/cache');
@@ -6,9 +7,20 @@ const common = require('./common');
 async function main() {
   try {
     if (core.getBooleanInput('use-cache')) {
-      const prefix = await common.getCachePrefix();
-      const name = prefix + github.context.runId;
-      await cache.saveCache([await common.getZigCachePath()], name);
+      const cache_path = await common.getZigCachePath();
+
+      let accessible = true;
+      try {
+        await fs.access(cache_path, fs.constants.R_OK);
+      } catch {
+        accessible = false;
+      }
+
+      if (accessible) {
+        const prefix = await common.getCachePrefix();
+        const name = prefix + github.context.runId;
+        await cache.saveCache([cache_path], name);
+      }
     }
   } catch (err) {
     core.setFailed(err.message);