Is try-with-resource fundamentally unsafe?

I am using try-with-resources, introduced in Java 7. This program downloads several HTTP resources and compresses them.

import java.io.*;
import java.net.*;
import java.util.zip.GZIPOutputStream;

class Main {
    private static byte[] downloadAndCompress(URL url) throws IOException {
        ByteArrayOutputStream byteOutput = new ByteArrayOutputStream();
        HttpURLConnection connection = (HttpURLConnection)url.openConnection();
        try(
            Closeable closeConnection = () -> connection.disconnect();
            OutputStream gzipOutput = new GZIPOutputStream(byteOutput);
        ) {
            connection.connect();
            byte[] buffer = new byte[1024];
            int bytesRead;
            while (0 <= (bytesRead = connection.getInputStream().read(buffer))) {
                gzipOutput.write(buffer, 0, bytesRead);
            }
        }
        return byteOutput.toByteArray();

    }

    public static void main(String[] args) throws Exception {
        for (int i = 0; i < 10; i++) {
            URL url = new URL("http://example.com?" + i);
            try {
                downloadAndCompress(url);
                // TODO: do something with result
            } catch (IOException e) {
                System.err.println("Failed to download " + url + ": " + e);
            }
        }
    }
}

I wondered what would happen if (1) the request failed and (2) writing the gzip trailer exceeded available heap memory.

So I rewrote downloadAndCompare to test:

        HttpURLConnection connection = (HttpURLConnection)url.openConnection();
        try(
            Closeable closeConnection = () -> connection.disconnect();
            OutputStream gzipOutput = new GZIPOutputStream(byteOutput) {
                public void close() { throw new OutOfMemoryError(); }
            };
        ) {
            throw new IOException("failed to download");
        }

Running it yields

Failed to download http://example.com?0: java.io.IOException
Failed to download http://example.com?1: java.io.IOException
Failed to download http://example.com?2: java.io.IOException
Failed to download http://example.com?3: java.io.IOException
Failed to download http://example.com?4: java.io.IOException
Failed to download http://example.com?5: java.io.IOException
Failed to download http://example.com?6: java.io.IOException
Failed to download http://example.com?7: java.io.IOException
Failed to download http://example.com?8: java.io.IOException
Failed to download http://example.com?9: java.io.IOException

It appears that try-with-resources suppresses all Throwables encountered in closing resources, be they OutOfMemoryError, InterruptedException, or StackOverflowError.

I read that it is a very bad thing to continue after OOM and other errors happen.

How does that reconcile with this language construct? Is ignoring OOM fine? Is try-with-resource safe to use?